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Libcint is a library designed for the evaluation of analytical integrals for Gaussian type orbitals. It prioritizes simplicity, ease of use, and efficiency for the development of quantum chemistry programs. In the release of version 6.0, Libcint supports the computation of integrals for various operators, such as overlap, Coulomb, Gaunt, Breit, attenuated Coulomb, Slater-type geminals, and Yukawa potential, as well as arbitrary orders of derivatives for these operators. To enhance the usability of the library, Libcint provides a uniform function signature for all integral functions. A code generator is included to automate the implementation of new integrals. To achieve better performance on modern central processing unit architectures, the library employs explicit single instruction multiple data parallelization in the code implementation. [ABSTRACT FROM AUTHOR]

Wavelets and multiwavelets have lately been adopted in quantum chemistry to overcome challenges presented by the two main families of basis sets: Gaussian atomic orbitals and plane waves. In addition to their numerical advantages (high precision, locality, fast algorithms for operator application, linear scaling with respect to system size, to mention a few), they provide a framework that narrows the gap between the theoretical formalism of the fundamental equations and the practical implementation in a working code. This realization led us to the development of the Python library called VAMPyR (Very Accurate Multiresolution Python Routines). VAMPyR encodes the binding to a C++ library for multiwavelet calculations (algebra and integral and differential operator application) and exposes the required functionality to write a simple Python code to solve, among others, the Hartree–Fock equations, the generalized Poisson equation, the Dirac equation, and the time-dependent Schrödinger equation up to any predefined precision. In this study, we will outline the main features of multiresolution analysis using multiwavelets and we will describe the design of the code. A few illustrative examples will show the code capabilities and its interoperability with other software platforms. [ABSTRACT FROM AUTHOR]

This paper presents an efficient numerical method for solving nonlinear stochastic delay integro-differential equations based on block pulse functions. Firstly, the equation is transformed into an algebraic system by the integral delay operator matrixes of block pulse functions. Then, error analysis is conducted on the method. Finally, some numerical examples are provided to validate the method. This work provides numerical solutions for the stochastic delay integro-differential equations by global approximation method. This method has the advantages of simple calculation and higher error accuracy. [ABSTRACT FROM AUTHOR]

In this paper, we first prove a generalized fractional version of Hermite-Hadamard-Mercer type inequalities using h-convex functions by means of ψ-Hilfer fractional integral operators. Then, we give new identities of this type with special functions depending on ψ. Moreover, we establish some new fractional integral inequalities connected with the right- and left-hand sides of Hermite-Hadamard-Mercer inequalities involving differentiable mappings whose absolute values of the derivatives are h-convex. For the development of these novel integral inequalities, we utilize h-Mercer inequality and Hölder's integral inequality. These results offer the significant advantage of being convertible into classical integral inequalities and Riemann–Liouville fractional integral inequalities for convex functions, s-convex functions, and P-convex functions. [ABSTRACT FROM AUTHOR]

The article reveals new applications of the four-parameter Mittag-Leffler function (MLF) in geometric function theory (GFT), using fractional calculus notions. The purpose of this study is to propose and explore a new integral operator of order λ using fractional calculus and the four-parameter MLF. The techniques of differential subordination theory are employed in order to derive certain univalence conditions for the newly defined fractional calculus operator involving the Mittag-Leffler function. In the proved theorems and corollaries of the paper, it is specified that the fractional integral operator of the four parameter MLF satisfies the conditions to be starlike and convex. It is also proved that the newly defined operator is a starlike, convex, and close-to-convex function of positive and negative orders, respectively. The geometric properties demonstrated for the fractional integral of the four-parameter MLF show that this function could be a valuable resource for developing the study of geometric functions theory, differential subordination, and superordination theory. [ABSTRACT FROM AUTHOR]

Let μ be a finite measure, $ T:L_1(\mu)\to X $ T : L 1 (μ) → X be an operator into a Banach space X, and $ I:L_\infty (\mu)\to L_1(\mu) $ I : L ∞ (μ) → L 1 (μ) be the natural inclusion. A well-known theorem due to Grothendieck states that T is representable if and only $ T\circ I $ T ∘ I is nuclear. In a 2022 paper we gave a multilinear version of this theorem replacing nuclearity by the weaker property that we call the left integral $ \ell _1 $ ℓ 1 -factorization property. Here we prove the rather surprising result that the multilinear version is also true for nuclearity. As an application, we show that the composition $ P\circ T $ P ∘ T of an integral operator T with a polynomial P whose Aron–Berner extension to the bidual takes values in the original range space is nuclear. This extends (and strengthens) to the polynomial setting a result on composition of operators also due to Grothendieck. [ABSTRACT FROM AUTHOR]

One of the strategies used in some countries to contain the COVID-19 epidemic has been the test-and-isolate policy, generally coupled with contact tracing. Such strategies have been examined in several simulation models, but a theoretical analysis of their effectiveness in simple epidemic model is, to our knowledge, missing. In this paper, we present four epidemic models of either SIR or SEIR type, in which it is assumed that at fixed times the whole population (or a part of the population) is tested and, if positive, isolated. We find the conditions for an epidemic to go extinct under such a strategy; for these types of models we provide an appropriate definition of R 0 , that can be computed either analytically or numerically. Finally, we show numerically that the final-size relation of SIR models approximately holds for the four models, over a large parameter range. [ABSTRACT FROM AUTHOR]

In this work, we prove a threshold theorem for the 2D Navier-Stokes equations posed on the periodic channel, T × [ - 1 , 1 ] , supplemented with Navier boundary conditions ω | y = ± 1 = 0 . Initial datum is taken to be a perturbation of Couette in the following sense: the shear component of the perturbation is assumed small (in an appropriate Sobolev space) but importantly is independent of ν . On the other hand, the nonzero modes are assumed size O (ν 1 2) in an anisotropic Sobolev space. For such datum, we prove nonlinear enhanced dissipation and inviscid damping for the resulting solution. The principal innovation is to capture quantitatively the inviscid damping, for which we introduce a new Singular Integral Operator which is a physical space analogue of the usual Fourier multipliers which are used to prove damping. We then include this SIO in the context of a nonlinear hypocoercivity framework. [ABSTRACT FROM AUTHOR]

To study the influence of the moving front of the infected interval and the spatial movement of individuals on the spreading or vanishing of infectious disease, we consider a nonlocal susceptible–infected–susceptible (SIS) reaction–diffusion model with media coverage, hospital bed numbers and free boundaries. The principal eigenvalue of the integral operator is defined, and the impacts of the diffusion rate of infected individuals and interval length on the principal eigenvalue are analyzed. Furthermore, sufficient conditions for spreading and vanishing of the disease are derived. Our results show that large media coverage and hospital bed numbers are beneficial to the prevention and control of disease. The difference between the model with nonlocal diffusion and that with local diffusion is also discussed and nonlocal diffusion leads to more possibilities. [ABSTRACT FROM AUTHOR]

In this paper, some Hermite-Hadamard integral inequalities and Hermite-Hadamard-Fejér integral inequalities involving Atangana-Baleanu fractional integral operators via $ (h_ {1}, h_ {2})- $convex functions and $ (h_ {1}, h_ {2})- $concave functions are established. Then, according to an integral equation with Atangana-Baleanu fractional integral operators, some Hermite-Hadamard integral inequalities for second order differentiable convex maps are given. [ABSTRACT FROM AUTHOR]

Due to applicability of mathematical inequalities in control systems, actuarial science, information theory and its utilization in other sciences, several researchers are inclined to prove their refinements and generalizations. In the study of mathematical inequalities, convex functions (CFs) and the derived classes of CFs are the most studied objects. On the other hand, fractional calculus has emerged as an indispensable tool in Engineering, Physics, and Mathematics, with widespread applications. The recently introduced Cr-order based class of interval-valued functions (IVFs) has shown applications in information theory. In this paper, we aim to investigate mathematical inequalities for geometrically arithmetically Cr-convex functions (GA-Cr-CFs) via interval-valued Hadamard fractional integral operators (IVHFIOs). More precisely, we study the Hermite–Hadamard–Mercer type inequalities and the weighted Hermite–Hadamard–Mercer type inequalities involving GA-Cr-CFs and IVHFIOs. Under particular assumptions, the proved results produce inequalities from the recent related literature. Furthermore, we establish connections between geometrically arithmetically convex functions (GA-CFs) and self information function of each event with a given probability in a complete information system. At the end, we demonstrate the role of fractional order of IVHFIOs in producing the refinements of the inequalities for the usual integrals. Thus, the current study provides both the extension of theoretical literature as well as application aspects. [ABSTRACT FROM AUTHOR]

The purpose of this article is to provide a number of Hermite–Hadamard and Fejér type integral inequalities for a class of h$$ h $$‐superquadratic functions. We then develop the fractional perspective of inequalities of Hermite–Hadamard and Fejér types by use of the Riemann–Liouville fractional integral operators and bring up with few particular cases. Numerical estimations based on specific relevant cases and graphical representations validate the results. Another motivating component of the study is that it is enriched with applications of modified Bessel function of first type, special means, and moment of random variables by defining some new functions in terms of modified Bessel function and considering uniform probability density function. The results in this paper have not been initiated before in the frame of h$$ h $$‐superquadraticity. We are optimistic that this effort will greatly stimulate and encourage additional research. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the existence of multiplicity of positive solutions to a new generalized Riemann–Liouville type fractional Fisher‐like equation on a semi‐infinite interval equipped with nonlocal multipoint boundary conditions involving Riemann–Liouville fractional derivative and integral operators. The existence of at least two positive solutions for the given problem is established by using the concept of complete continuity and iterative positive solutions. We show the existence of at least three positive solutions to the problem at hand by applying the generalized Leggett–Williams fixed‐point theorem due to Bai and Ge [Z. Bai, B. Ge, Existence of three positive solutions for some second‐order boundary value problems, Comput. Math. Appl. 48 (2014) 699‐70]. Illustrative examples are constructed to demonstrate the effectiveness of the main results. It has also been indicated in Section 5 that some new results appear as special cases by choosing the parameters involved in the given problem appropriately. [ABSTRACT FROM AUTHOR]

In this paper, we consider weighted jump and variational inequalities of truncated singular integral operator with rough kernel TΩ,β,휀f(x) =∫|y|>휀 Ω(y) |y|n−βf(x − y)dy, where the kernel Ω ∈ Ls(핊n−1)(s > 1) satisfies the cancellation condition and the homogeneous condition of degree 0 and 0 ≤ β < n. This kind of singular integral appears in the approximation of the surface quasi-geostrophic (SQG) equation from the generalized SQG equation. We establish the (Lp(ωp),Lq(ωq)) estimate of the jump and variational inequalities of the families {TΩ,β,휀}휀>0 for 1 q = 1 p −β n. Moreover, one can get the weighted Lp boundedness of the Calderón–Zygmund operator by letting β → 0+. [ABSTRACT FROM AUTHOR]

The dyadic representation of any singular integral operator, as an average of dyadic model operators, has found many applications. While for many purposes it is enough to have such a representation for a "suitable class" of test functions, we show that, under quite general assumptions (essentially minimal ones to make sense of the formula), the representation is actually valid for all pairs (f,g) ∈ Lp(ℝd) × Lp′(ℝd), not just test functions. [ABSTRACT FROM AUTHOR]

This paper is an offspring of the previous study on Herz spaces. A new characterization of Morrey-Herz spaces is given. As applications, the boundedness of various operators is obtained. For example, higher-order commutators generated by singular integral operators and BMO functions are proved to be bounded on Morrey-Herz spaces. The theory of Morrey-Herz-Hardy spaces is also developed. [ABSTRACT FROM AUTHOR]

Let T be a bilinear vector-valued singular integral operator satisfies some mild regularity conditions, which may not fall under the scope of the theory of standard Calderón–Zygmund classes. For any b → = (b 1 , b 2) ∈ (CMO (R n)) 2 , let [ T , b j ] e j (j = 1 , 2) , [ T , b → ] α be the commutators in the j-th entry and the iterated commutators of T, respectively. In this paper, for all p0 > 1, p 0 2 < p < ∞ , and p0 ≤ p1, p2 < ∞ with 1/p = 1/p1 + 1/p2, we prove that [ T , b j ] e j and [ T , b → ] α are weighted compact operators from L p 1 (w 1) × L p 2 (w 2) to L p (ν w → ) , where w → = (w 1 , w 2) ∈ A p → / p 0 and ν w → = w 1 p / p 1 w 2 p / p 2 . As applications, we obtain the weighted compactness of commutators in the j-th entry and the iterated commutators of several kinds of bilinear Littlewood–Paley square operators with some mild kernel regularity, including bilinear g function, bilinear g*λ function and bilinear Lusin's area integral. In addition, we also get the weighted compactness of commutators in the j-th entry and the iterated commutators of bilinear Fourier multiplier operators, and bilinear square Fourier multiplier operators associated with bilinear g function, bilinear g*λ function and bilinear Lusin's area integral, respectively. [ABSTRACT FROM AUTHOR]

In this paper, we consider the jump and variational inequalities of truncated singular integral operator with rough kernel T Ω , β , ε f (x) = ∫ ∣ y ∣> ε Ω (y) ∣ y ∣ n − β f (x − y) d y , where the kernel Ω (L (log + L) 2 ) n n − β (S n − 1) satisfies the vanishing condition and the homogeneous condition of degree 0. This kind of singular integral appears in the approximation of the surface quasi-geostrophic (SQG) equation from the generalized SQG equation. We establish the (Lp, Lq) estimate of the jump and variational inequalities of the families {TΩ,β,ε}ε>0 for 1 q = 1 p − β n and 0 < β < 1. Moreover, one can get the Lp boundedness of the Calderón–Zygmund operator with the same kernel by letting β → 0+. [ABSTRACT FROM AUTHOR]

We establish the subadditivity of strongly operator convex functions on (0 , ∞) and (− ∞ , 0). By utilizing the properties of strongly operator convex functions, we derive the subadditivity property of operator monotone functions on (− ∞ , 0). We introduce new operator inequalities involving strongly operator convex functions and weighted operator means. In addition, we explore the relationship between strongly operator convex and Kwong functions on (0 , ∞). Moreover, we study strongly operator convex functions on (a , ∞) with − ∞ < a and on the left half-line (− ∞ , b) with b < ∞. We demonstrate that any nonconstant strongly operator convex function on (a , ∞) is strictly operator decreasing, and any nonconstant strongly operator convex function on (− ∞ , b) is strictly operator monotone. Consequently, for a strongly operator convex function g on (a , ∞) or (− ∞ , b) , we provide lower bounds for | g (A) − g (B) | whenever A − B > 0. [ABSTRACT FROM AUTHOR]

In this article, we propose a numerical method for a general form of nonlinear cordial Volterra integral equations. We discuss conditions that under them the problem has solutions. Since the existence of solutions for the problem depends on the solvability of a scalar equation and also a linear form of the problem, then we employ quasilinearization technique in which solving a nonlinear problem is reduced to solve a sequence of linear equations. The existence of solutions of linear equations and their quadratically convergence to the solutions of the nonlinear problem is considered. For the numerical solution of the produced linear equations we apply Legendre-collocation method along with a regularization technique for the quadrature formulas. We discuss the error analysis of the collocation method considering that the cordial Volterra integral operators are noncompact. To test the efficiency and accuracy of the proposed method, the solution of different cases of numerical examples are reported. [ABSTRACT FROM AUTHOR]

We study a special type of infinite direct sums E (X) which can be seen as the amalgam spaces characterized by a local component given by a countable family X = X α α ∈ I of quasi-normed function spaces and by a global component E, which is a quasi-normed sequence space. We characterize some fundamental properties of E (X) such as completeness, Köthe-duality, order continuity and the Fatou property. We also provide its Banach function space characterization. Then, we apply our general results to the appropriate amalgamations of Lorentz (Orlicz) function spaces and Lebesgue sequence spaces. Moreover, for the Lorentz-type amalgams, we derive interpolation results and prove the boundedness of a class of sublinear integral operators whose kernels satisfy a size condition. [ABSTRACT FROM AUTHOR]

In this article, we obtained the global boundedness for the bilinear Fourier integral operators with rough Hörmander class on the product of Hardy spaces. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a class of self-adjoint operators that contains the left- and right-sided general fractional derivatives with the Sonin kernels. Then a fractional Sturm-Liouville problem with these operators and the boundary conditions in terms of the left- and right-sided general fractional derivatives and integrals is investigated. In particular, we show that the eigenvalues of the fractional Sturm-Liouville problem are real numbers and the eigenfunctions corresponding to distinct eigenvalues are orthogonal under a certain weighted scalar product. Finally, we discuss a particular case of the fractional Sturm-Liouville problem and deduce its solution in terms of the fractional Chebyshev functions. [ABSTRACT FROM AUTHOR]

We innovatively introduce a new group of integral operators called multiplicative k-Atangana–Baleanu fractional integrals. Following the path of this research, we discuss their ∗integrability, continuity, boundedness together with linearity, and successfully construct two Hermite–Hadamard–Mercer inequalities employing this multiplicative fractional integrals, focusing on endpoint- and midpoint-type, respectively. Subsequently, we further propose three identities, involving trapezoid-Mercer-, midpoint-Mercer-, and parameterized-Mercer-type, and combining the function Λ∗ is multiplicatively convex or, for some fixed q > 1, the function (lnΛ∗)q is convex, and we formulate a series of corresponding fractional Mercer-type inequalities. Intended to enhance the readers’ deeper understanding of the results, we offer two instances accompanied by graphical representations, facilitating the validity of the inequalities gained in the current paper. Finally, some applications in multiplicative differential equation, the quadrature formula and special means are presented as well. [ABSTRACT FROM AUTHOR]

The mixed BVP for a compressible Stokes system of PDEs with variable viscosity is considered in a bounded domain of three dimensions. Based on a specially constructed parametrix (Levi function), the problem is reduced to the united boundary‐domain integro‐differential or integral equations (BDIDEs or BDIEs). The BDIDEs are to be supplemented by the original boundary conditions, thus constituting boundary‐domain integro‐differential problems (BDIDPs). The BDIDPs/BDIEs contain integral operators defined on the domain under consideration as well as potential‐type operators defined on open submanifolds of the boundary and acting on the trace and/or traction of the unknown solution or on an auxiliary function. Solvability, solution uniqueness, equivalence of the BDIDPs/BDIEs to the original BVP, and invertibility of the associated operators are investigated in appropriate Sobolev spaces. [ABSTRACT FROM AUTHOR]

In this paper, we consider a family of random linear operators that arises in the construction of a probabilistic representation of the resolvent of the two-dimensional Laplacian. It is shown that with probability 1 the operators of this family are integral operators in L2(ℝ2). The properties of the kernels of the corresponding operators are also studied. [ABSTRACT FROM AUTHOR]

We consider random operators arising when one constructs a probabilistic representation of the resolvent of an operator - 1 2 d dx b 2 x d dx + V x . We prove that with probability one these operators are linear integral operators and study properties of their kernels. [ABSTRACT FROM AUTHOR]

In this paper, the authors establish the three‐parameter Triebel–Lizorkin spaces and characterize these spaces as the intersection of two flag Triebel–Lizorkin spaces by applying the discrete Littlewood–Paley–Stein analysis. Moreover, they obtain the boundedness of product singular integral operators on the three‐parameter Triebel–Lizorkin spaces. [ABSTRACT FROM AUTHOR]

In this work, we give a qualitative study on the existence of positive solutions for local and nonlocal elliptic integro-differential quasilinear systems, by using the concept of super- and subsolutions combined with Schauder's fixed point theorem. [ABSTRACT FROM AUTHOR]

We prove the inequalities of the weighted Hermite–Hadamard type the and Hermite–Hadamard–Mercer type for an extremely rich class of geometrically arithmetically-h-convex functions (GA-h-CFs) via generalized Hadamard–Fractional integral operators (HFIOs). The two generalized fractional integral operators (FIOs) are Hadamard proportional fractional integral operators (HPFIOs) and Hadamard k-fractional integral operators (HKFIOs). Moreover, we also present the results for subclasses of GA-h-CFs and show that the inequalities proved in this paper unify the results from the recent related literature. Furthermore, we compare the two generalizations in view of the fractional operator parameters that contribute to the generalizations of the results and assess the better approximation via graphical tools. Finally, we present applications of the new inequalities via HPFIOs and HKFIOs by establishing interpolation relations between arithmetic mean and geometric mean and by proving the new upper bounds for the Tsallis relative operator entropy. [ABSTRACT FROM AUTHOR]

Several integral inequalities of the Fejér type are derived, incorporating the generalized Mittag-Leffler function alongside the associated fractional integral operator. Consequently, generalizations of known results are achieved. [ABSTRACT FROM AUTHOR]

We give investigations on the approximation order of translation networks produced by the convolution translation operators defined on a Jacobi cone and the surface cone. We deal with the convolution translation from the view of Fourier analysis, express the translation operator with orthogonal basis and provide a sufficient condition to ensure the density for the translation networks. Based on these facts, we construct with the near best approximation operator and the Gauss integral formula two kinds of translation network operators and show their approximation orders in the best polynomial approximation. [ABSTRACT FROM AUTHOR]

An approximate algorithm for calculating integral convolution operators that arise when estimating barrier options in Lévy models using the Wiener–Hopf method is constructed. Additionally, the possibility of applying machine learning methods (artificial neural networks) to approximating a special type of integrals, which are a key element in the construction of approximate formulas for the considered Wiener–Hopf integral operators, is studied. The main idea is to expand the price function in the Fourier series and transform the integration contour for each term of the Fourier series. As a result, we obtain a set of typical integrals that depend on the Wiener–Hopf factors but are independent of the price function; then, the most computationally expensive part of the numerical method is reduced to calculating these integrals. Since they only need to be calculated once, rather than at each iteration as was the case in standard implementations of the Wiener–Hopf method, this will significantly speed up the calculations. Moreover, a neural network can be trained to calculate typical integrals. The proposed approach is especially efficient for spectrally one-sided Lévy processes for which explicit Wiener–Hopf factorization formulas are known. In this case, we obtain formulas convenient for calculations by integrating along the cut. The main advantage of including neural networks in the computational scheme is the ability to perform calculations on a nonuniform grid. Such a hybrid numerical method can successfully compete with classical methods for calculating convolutions in similar problems using the fast Fourier transform. Computational experiments show that neural networks with one hidden layer of 20 neurons are able to efficiently cope with the problems of approximating the auxiliary integrals under consideration. [ABSTRACT FROM AUTHOR]

The paper studies integral operators on the interval of real line which naturally arise in some problems in the theory of integral equations and mathematical physics. We study boundedness in weighted Lebesgue spaces: Sufficient and necessary conditions for boundedness are given. Also, special important particular cases of operators and spaces are considered as examples. We construct identity approximation within the framework of the class of operators under study, and two different approaches are given. [ABSTRACT FROM AUTHOR]

We introduce and study Hausdorff–Zhu operators over the unit ball in ℂn$$ {\mathrm{\mathbb{C}}}&#x0005E;n $$. We give sufficient conditions for boundedness of such operators in Möbius invariant spaces, weighted Lebesgue and Bergman spaces, and Hardy spaces on the unit ball. In the framework of the Lebesgue spaces, we also provide necessity conditions for boundedness. Approximation of the identity by Hausdorff operators is also considered within Lebesgue space with a Möbius invariant Haar measure. [ABSTRACT FROM AUTHOR]

We prove the existence of a (d-2)-dimensional purely unrectifiable set upon which a family of even singular integral operators is bounded. [ABSTRACT FROM AUTHOR]

In this paper, we study a generalized Biot–Savart law for suitable velocity that possibly diverges at infinity, and then show its application to the 2D general incompressible inviscid fluids. We first prove the generalized Biot–Savart law for the active scalar equations in a discrete rotational symmetry framework, which allows the velocity grow almost linearly at infinity. Based on this, we further obtain a unique global symmetric solution to Euler equation under the Yudovich type regularity. Additionally, we investigate the local well-posedness for the Boussnesq equation, SQG equation, and especially for the IPM equation which enjoys particular symmetric property in our setting. The proof mainly relies on the Fourier model analysis and some refined estimates to the singular integral operator. [ABSTRACT FROM AUTHOR]

The goal of this study is to develop numerous Hermite–Hadamard–Mercer (H–H–M)-type inequalities involving various fractional integral operators, including classical, Riemann–Liouville (R.L), k-Riemann–Liouville (k-R.L), and their generalized fractional integral operators. In addition, we establish a number of corresponding fractional integral inequalities for three-times differentiable convex functions that are connected to the right side of the H–H–M-type inequality. For these results, further remarks and observations are provided. Following that, a couple of graphical representations are shown to highlight the key findings of our study. Finally, some applications on special means are shown to demonstrate the effectiveness of our inequalities. [ABSTRACT FROM AUTHOR]

The notion of the fuzzy set was incorporated into geometric function theory in recent years, leading to the emergence of fuzzy differential subordination theory, which is a generalization of the classical differential subordination notion. This article employs a new integral operator introduced using the class of meromorphic functions, the notion of convolution, and the Hurwitz–Lerch Zeta function for obtaining new fuzzy differential subordination results. Furthermore, the best fuzzy dominants are provided for each of the fuzzy differential subordinations investigated. The results presented enhance the approach to fuzzy differential subordination theory by giving new results involving operators in the study, for which starlikeness and convexity properties are revealed using the fuzzy differential subordination theory. [ABSTRACT FROM AUTHOR]

We define new classes of meromorphic p-valent convex functions, respectively, meromorphic close-to-convex functions, by using an extension of Wanas operator in order to study the preservation properties of these classes, when a well-known integral operator is used. We find the conditions which allow this operator to preserve the classes mentioned above, and we will remark the symmetry between these classes. [ABSTRACT FROM AUTHOR]

The application of a fractional-order controller (FOC) using the Caputo–Fabrizio representation in the automatic voltage regulation (AVR) system of a synchronous generator is shown in this paper. The mathematical model of the system is created and the adequacy of the model is confirmed. The efficiency of the proposed regulator in different operating regimes is demonstrated. In particular, the proposed controller improves voltage regulation in a wide range of changes in the coordinates that characterize the power system operation mode, and it increases the system's robustness to both uncertainties and nonlinearities that often occur in power systems. The synthesized fractional-order regulator provides higher response and control accuracy compared to traditional regulators used in automatic voltage regulation (AVR) systems. [ABSTRACT FROM AUTHOR]

This article investigates certain q-analogue of the fractional Agarwal integral operator and its application to a class of polynomials and a series of functions. By utilizing various types of q-Bessel functions, the fractional q-Agarwal integral has been discussed and formulated in a series expression form involving q-shifted factorials and gamma functions. Moreover, certain results and applications of the q-Bessel theory are reported by establishing suitable forms of the fractional integral. Furthermore, the fractional Agarwal integral has been evaluated for some multiple power series formulas. Meanwhile, some desirable results involving q-generating Heine's series of the first type are provided. Over and above, certain conclusions associated with various exponential, hyperbolic sine and cosine functions are analysed. [ABSTRACT FROM AUTHOR]

The Choquet integral is a fuzzy measure that serves as an effective aggregation operator for combining a limited number of components into a single set. In 1978, Hamacher introduced the Hamacher t-norm and t-conorm, an expanded version of algebraic t-norms. In this article, we present the aggregation operators for the Choquet integral that utilize the Hamacher t-norms to handle the theory of complex intuitionistic fuzzy values. These operators include the complex intuitionistic fuzzy Hamacher Choquet integral averaging and geometric operators. Additionally, an analysis is conducted on the attributes and special situations of the suggested methodologies. In addition, a novel approach is presented, utilizing newly developed operators for solving multi-attribute decision-making issues with complex intuitionistic fuzzy values. The operational stages of this strategy are thoroughly presented. Finally, we conducted a comprehensive comparison between the proposed methodology and existing approaches, using illustrative examples to validate the effectiveness and demonstrate the advantages of the proposed methods. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to find the sufficient conditions for the subclasses of analytic functions associated with Wright distribution series to be in subclasses of univalent functions and inclusion relations for such subclasses in the open unit disk D. Further, we consider the properties of integral operator related to Wright distribution series. [ABSTRACT FROM AUTHOR]

Into this article, we consider the subclasses Vj, Vj,μ and ∑j(p), with j=2,3,..., and generalize univalence conditions for the integral operator Gαi,β of the analytic functions g in the exterior unit disk. We want to see if some univalent conditions for analytic functions obtained on the interior unit disk can be extended on the exterior unit disk, so we make use of the usual transformation g(z)=1f(1/z). [ABSTRACT FROM AUTHOR]

AbstractA novel analytical technique based on singular integral operators (SIO) is presented to study the strip electric-magnetic polarization saturation (EMPS) model in magneto-electro-elastic (MEE) solids with two unequal collinear cracks. Unknown semipermeable crack-face conditions and saturated zone lengths are evaluated using iterative techniques and the obtained new analytical solutions for dislocation densities. Numerical studies of fracture parameters are conducted with respect to variations in electrical loading, inter crack space distance and crack-length ratio. The accuracy and efficacy of the SIO method are validated against published results for cases with two equal collinear cracks and center crack. [ABSTRACT FROM AUTHOR]

We study the compactness of commutator of a locally integrable function and an oscillatory singular integral operator defined by a real-valued polynomial and a kernel function satisfying the Hölder condition. We show that such a commutator is compact from L p {L^{p}} to L q {L^{q}} if and only if the locally integrable function is the sum of a constant and a function in certain Lebesgue space. [ABSTRACT FROM AUTHOR]

Applying the operator of q -difference, we examine the convolution properties of the subclasses MS ζ , q r , p (A , B) and M K ζ , q r , p (A , B) of p-valent meromorphic functions defined in the punctured open-unit disc. We derived specific inclusion features and coefficient estimates for functions that fall into these subclasses. Additionally, connections between the results presented here and those discovered in earlier papers are emphasized. [ABSTRACT FROM AUTHOR]

In this paper, we studied a mathematical model for honeybee population diseases under the influence of seasonal environments on the long-term dynamics of the disease. The model describes the dynamics of two different beehives sharing a common space. We computed the basic reproduction number of the system as the spectral radius of either the next generation matrix for the autonomous system or as the spectral radius of a linear integral operator for the non-autonomous system, and we deduced that if the reproduction number is less than unity, then the disease dies out in the honeybee population. However, if the basic reproduction number is greater than unity, then the disease persists. Finally, we provide several numerical tests that confirm the theoretical findings. [ABSTRACT FROM AUTHOR]