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In this paper, the fractional-order Chelyshkov functions (FCHFs) and Riemann-Liouville fractional integrals are utilized to find numerical solutions to fractional delay differential equations, by transforming the problem into a system of algebraic equations with unknown FCHFs coefficients. An error bound of FCHFs approximation is estimated and its convergence is also demonstrated. The effectiveness and accuracy of the presented method are established through several examples. The resulting solution is accurate and agrees with the exact solution, even if the exact solution is not a polynomial. Moreover, comparisons between the obtained numerical results and those recently reported in the literature are shown. [ABSTRACT FROM AUTHOR]

In this article, a new numerical algorithm for solving a 1-dimensional (1D) and 2-dimensional (2D) time-fractional diffusion equation is proposed. The Sinc-Galerkin scheme is considered for spatial discretization, and a higher-order finite difference formula is considered for temporal discretization. The convergence behavior of the methods is analyzed, and the error bounds are provided. The main objective of this paper is to propose the error bounds for 2D problems by using the Sinc-Galerkin method. The proposed method in terms of convergence is studied by using the characteristics of the Sinc function in detail with optimal rates of exponential convergence for 2D problems. Some numerical experiments validate the theoretical results and present the efficiency of the proposed schemes. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to consider the multiple birth properties for multi-type Markov branching processes. We first construct a new multi-dimensional Markov process based on the multi-type Markov branching process, which can reveal the multiple birth characteristics. Then the joint probability distribution of multiple birth of multi-type Markov branching process until any time t is obtained by using the new process. Furthermore, the probability distribution of multiple birth until the extinction of the process is also given. [ABSTRACT FROM AUTHOR]

This study explores the extension of Milne-type inequalities to the realm of Katugampola fractional integrals, aiming to broaden the analytical tools available in fractional calculus. By introducing a novel integral identity, we establish a series of Milne-type inequalities for functions possessing extended s-convex first-order derivatives. Subsequently, we present an illustrative example complete with graphical representations to validate our theoretical findings. The paper concludes with practical applications of these inequalities, demonstrating their potential impact across various fields of mathematical and applied sciences. [ABSTRACT FROM AUTHOR]

In this paper, a class of fractional Sturm–Liouville advection–dispersion equations with instantaneous and noninstantaneous impulses is considered, in particular, the nonlinearities discussed here include Caputo fractional derivatives. Since the nonlinear terms contain fractional derivatives, this problem does not directly have variational structure, we need to combine critical point theory and an iterative method to deal with such problems. Finally, the existence of at least one nontrivial solution is proved by the mountain pass theorem and the iterative method. At the same time, an example is given to illustrate the main result. [ABSTRACT FROM AUTHOR]

This paper deals with the following nonlinear elliptic equation: − Δ u = Q (| y ′ | , y ″) u N + 2 N − 2 , u > 0 , in R N , u ∈ D 1 , 2 (R N) , where (y ′ , y ″) ∈ R 2 × R N − 2 , N ≥ 5 , Q (| y ′ | , y ″) is a bounded nonnegative function in R 2 × R N − 2 . By using the local Pohozaev identities we prove a nondegeneracy result for the positive solutions constructed in (Peng et al. in J. Differ. Equ. 267:2503–2530, 2019). [ABSTRACT FROM AUTHOR]

In this paper, we deal with an attraction–repulsion model with a logistic source as follows: { u t = Δ u − χ ∇ ⋅ (u ∇ v) + ξ ∇ ⋅ (u ∇ w) + μ u q (1 − u) in Q , v t = Δ v − α 1 v + β 1 u in Q , w t = Δ w − α 2 w + β 2 u in Q , where Q = Ω × R + , Ω ⊂ R 3 is a bounded domain. We mainly focus on the influence of logistic damping on the global solvability of this model. In dimension 2, q can be equal to 1 (Math. Methods Appl. Sci. 39(2):289–301, 2016). In dimension 3, we derive that the problem admits a global bounded solution when q > 8 7 . In fact, we transfer the difficulty of estimation to the logistic term through iterative methods, thus, compared to the results in (J. Math. Anal. Appl. 2:448 2017; Z. Angew. Math. Phys. 73(2):1–25 2022) in dimension 3, our results do not require any restrictions on the coefficients. [ABSTRACT FROM AUTHOR]

This paper uses the Galerkin method to investigate the existence of positive solution to a class of singular elliptic problems given by { − Δ u = λ 0 u β 0 + Λ 0 | ∇ u | γ 0 + f 0 (u) | x | α 0 + h 0 (x) , u > 0 in Ω , u = 0 on ∂ Ω , where Ω ⊂ R 2 is a bounded smooth domain, 0 < β 0 , γ 0 ≤ 1 , α 0 ∈ [ 0 , 2) , h 0 (x) ≥ 0 , h 0 ≠ 0 , h 0 ∈ L ∞ (Ω) , 0 < ∥ h 0 ∥ ∞ < λ 0 < Λ 0 , and f 0 are continuous functions. More precisely, f 0 has a critical exponential growth, that is, the nonlinearity behaves like exp (ϒ ‾ s 2) as | s | → ∞ , for some ϒ ‾ > 0 . [ABSTRACT FROM AUTHOR]

In this paper, the coupled system of sequential ψ-Hilfer fractional boundary value problems with non-instantaneous impulses is investigated. The existence results of the system are proved by means of topological degree theory. An example is constructed to demonstrate our results. Additionally, a graphical analysis is performed to verify our results. [ABSTRACT FROM AUTHOR]

In this paper, we examine the existence and uniqueness of solutions for a system of the first-order q-difference equations with multi-point and q-integral boundary conditions using various fixed point (fp) theorems. Also, we give two examples to support our results. [ABSTRACT FROM AUTHOR]

In this paper, the solvability of a new class of nonlocal boundary value problems for the Poisson equation is studied. Nonlocal conditions are specified in the form of a connection between the values of the unknown function at different points of the boundary. In this case, the boundary operator is determined using matrices of involution-type mappings. Theorems on the existence and uniqueness of solutions to the studied problems are proved. Using Green's functions of the classical Dirichlet and Neumann boundary value problems, Green's functions of the studied problems are constructed and integral representations of solutions to these problems are obtained. [ABSTRACT FROM AUTHOR]

In this work, we use two unique methodologies, the homotopy perturbation transform method and Yang transform decomposition method, to solve the fractional nonlinear seventh-order Kaup–Kupershmidt (KK) problem. The physical phenomena that arise in chemistry, physics, and engineering are mathematically explained in this equation, in particular, nonlinear optics, quantum mechanics, plasma physics, fluid dynamics, and so on. The provided methods are used to solve the fractional nonlinear seventh-order KK problem along with the Yang transform and fractional Caputo derivative. The results are significant and necessary for exploring a range of physical processes. This paper uses modern approaches and the fractional operator to develop satisfactory approximations to the offered problem. To solve the fractional KK equation, we first use the Yang transform and fractional Caputo derivative. He's and Adomian polynomials are useful to manage nonlinear terms. It is shown that the suggested approximate solution converges to the exact one. In these approaches, the results are calculated as convergent series. The key advantage of the recommended approaches is that they provide highly precise results with little computational work. The suggested approach results are compared to the precise solution. By comparing the outcomes with the precise solution using graphs and tables we can verify the efficacy of the offered strategies. Also, the outcomes of the suggested methods at various fractional orders are examined, demonstrating that the findings get more accurate as the value moves from fractional order to integer order. Moreover, the offered methods are innovative, simple, and quite accurate, demonstrating that they are effective for resolving differential equations. [ABSTRACT FROM AUTHOR]

In this paper, the existence of positive periodic solutions is studied for Liénard equation with a singularity of repulsive type, x ″ (t) + f (x (t)) x ′ (t) + φ (t) x μ (t) − 1 x γ (t) = e (t) , where f : (0 , + ∞) → R is continuous, which may have a singularity at the origin, the sign of φ (t) , e (t) is allowed to change, and μ, γ are positive constants. By using a continuation theorem, as well as the techniques of a priori estimates, we show that this equation has a positive T-periodic solution when μ ∈ [ 0 , + ∞) . [ABSTRACT FROM AUTHOR]

In this paper, we study the existence and uniqueness of positive solutions for a class of a fractional differential equation system of Riemann–Liouville type on infinite intervals with infinite-point boundary conditions. First, the higher-order equation is reduced to the lower-order equation, and then it is transformed into the equivalent integral equation. Secondly, we obtain the existence and uniqueness of positive solutions for each fixed parameter λ > 0 by using the mixed monotone operators fixed-point theorem. The results obtained in this paper show that the unique positive solution has good properties: continuity, monotonicity, iteration, and approximation. Finally, an example is given to demonstrate the application of our main results. [ABSTRACT FROM AUTHOR]

In this paper, we study fractional p 1 (x , ⋅) & p 2 (x , ⋅) -Laplacian Schrödinger-type equations for Robin boundary conditions. Under some suitable assumptions, we show that two solutions exist using the mountain pass lemma and Ekeland's variational principle. Then, the existence of infinitely many solutions is derived by applying the fountain theorem and the Krasnoselskii genus theory, respectively. Different from previous results, the topic of this paper is the Robin boundary conditions in R N ∖ Ω ‾ for fractional order p 1 (x , ⋅) & p 2 (x , ⋅) -Laplacian Schrödinger-type equations, including concave-convex nonlinearities, which has not been studied before. In addition, two examples are given to illustrate our results. [ABSTRACT FROM AUTHOR]

This paper focuses on introducing and examining the class of generalized strongly n-polynomial convex functions. Relationships between these functions and other types of convex functions are explored. The Hermite–Hadamard inequality is established for generalized strongly n-polynomial convex functions. Additionally, new integral inequalities of Hermite–Hadamard type are derived for this class of functions using the Hölder–İşcan integral inequality. The results obtained in this paper are compared with those known in the literature, demonstrating the superiority of the new results. Finally, some applications for special means are provided. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study a generalized Riemann–Liouville fractional differential equation and system with nonlocal boundary conditions. Firstly, some properties of the Green function are presented and then Lyapunov-type inequalities for a sequential ψ-Riemann–Liouville fractional boundary value problem are established. Also, the existence and uniqueness of solutions are proved by using Banach and Schauder fixed-point theorems. Furthermore, the existence and uniqueness of solutions to a sequential nonlinear differential system is established by means of Schauder's and Perov's fixed-point theorems. Examples are given to validate the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a scenario concerning a coupled nonlocal singular viscoelastic equation with sources and distributed delay terms. By establishing suitable conditions, we have proved that a finite-time blow-up occurs in the solution. [ABSTRACT FROM AUTHOR]

This paper focuses on exploring the existence of solutions for a specific class of FDEs by leveraging fixed point theorem. The equation in question features the Caputo fractional derivative of order 3 < u ˆ ≤ 4 and includes a term Θ (β , Z (β)) alongside boundary conditions. Through the application of a fixed point theorem in appropriate function spaces, we consider nonlocal conditions along with necessary assumptions under which solutions to the given FDE exist. Furthermore, we offer an example to illustrate the results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the study of equations of viscous compressible and heat-conducting full magnetohydrodynamic (MHD) steady flows in a horizontal layer under the gravitational force and a large temperature gradient across the layer. We assume as boundary conditions, periodic conditions in the horizontal directions, while in the vertical directions, slip-boundary is assumed for the velocity, vertical conditions for the magnetic field, and fixed temperature or fixed heat flux are prescribed for the temperature. The existence of stationary solution in a small neighborhood of a stationary profile close to hydrostatic state is obtained in Sobolev spaces as a fixed point of some nonlinear operator. [ABSTRACT FROM AUTHOR]

In this paper, we provide some appropriate conditions for the existence of solutions for a perturbed fractional neutral integro-differential system under the deformable derivative in a Banach space. Using the Banach contraction principle and Krasnoselskii's fixed point theorem, we establish some new existence theorems. Moreover, we provide two numerical examples to demonstrate the applicability of the theoretical results [ABSTRACT FROM AUTHOR]

In this paper, we obtain conditions of the solvability of the Riemann boundary value problem for sectionally analytic functions in multiply connected domains in Besov spaces embedded into the class of continuous functions. We indicate a new class of Cauchy-type integrals, which are continuous on a closed domain with continuous (not Hölder) density in terms of Besov spaces, and for which the Sokhotski–Plemelj formulas are valid. [ABSTRACT FROM AUTHOR]

In this paper we study the following nonlinear Schrödinger system: { − Δ u + α u = | u | p − 1 u + 2 q + 1 λ | u | p − 3 2 u | v | q + 1 2 , x ∈ R 3 , − Δ v + β v = | v | q − 1 v + 2 p + 1 λ | u | p + 1 2 | v | q − 3 2 v , x ∈ R 3 , u (x) → 0 , v (x) → 0 , as | x | → ∞ , where 3 ≤ p , q < 5 , α, β are positive parameters. We show that there exists λ k > 0 such that the equation has at least k radially symmetric sign-changing solutions and at least k seminodal solutions for each k ∈ N and λ ∈ (0 , λ k) . Moreover, we show the existence of a least energy radially symmetric sign-changing solution for each λ ∈ (0 , λ 0) where λ 0 ∈ (0 , λ 1 ] . [ABSTRACT FROM AUTHOR]

In this paper, we analyze the existence of solutions to a double-phase fractional equation of the Kirchhoff type in Musielak-Orlicz Sobolev space with variable exponents. Our approach is mainly based on the sub-supersolution method and the mountain pass theorem. [ABSTRACT FROM AUTHOR]

In the current research, some midpoint-type inequalities are generalized for co-ordinated convex functions with the help of generalized conformable fractional integrals. Moreover, some findings of this paper include results based on Riemann–Liouville fractional integrals and Riemann integrals. [ABSTRACT FROM AUTHOR]

The current paper introduces a novel generalization of cone metric spaces called type I and type II composed cone metric spaces. Therefore, examples of a type I and type II composed cone metric space, which is not a cone metric space, are given. We establish some results of fixed point precisely about Hardy–Rogers type contraction on C2CMS and provide examples. Finally, we present an application of our results and how our results solve the Fredholm integral equation of generalizing several existing and unique fixed point theorems. [ABSTRACT FROM AUTHOR]

A hybrid system interacts with the discrete and continuous dynamics of a physical dynamical system. The notion of a hybrid system gives embedded control systems a great advantage. The Langevin differential equation can accurately depict many physical phenomena and help researchers effectively represent anomalous diffusion. This paper considers a fractional hybrid Langevin differential equation, including the ψ-Caputo fractional operator. Furthermore, some novel boundaries selected are considered to be a problem. We used the Schauder and Banach fixed-point theorems to prove the existence and uniqueness of solutions to the considered problem. Additionally, the Ulam-Hyer stability is evaluated. Finally, we present a representative example to verify the theoretical outcomes of our findings. [ABSTRACT FROM AUTHOR]

In this paper, we first construct an integral identity associated with tempered fractional operators. By using this identity, we have found the error bounds for Simpson's second formula, namely Newton–Cotes quadrature formula for differentiable convex functions in the framework of tempered fractional integrals and classical calculus. Furthermore, it is also shown that the newly established inequalities are the extension of comparable inequalities inside the literature. [ABSTRACT FROM AUTHOR]

A novel analysis of the pulsatile nano-blood flow through a sinusoidal wavy channel, emphasizing the significance of diverse influences in the modelling, is investigated in this paper. This study examines the collective effects of slip boundary conditions, magnetic field, porosity, channel waviness, nanoparticle concentration, and heat source on nano-blood flow in a two-dimensional wavy channel. In contrast to prior research that assumed a constant pulsatile pressure gradient during channel waviness, this innovative study introduces a variable pressure gradient that significantly influences several associated parameters. The mathematical model characterising nano-blood flow in a horizontally wavy channel is solved using the perturbation technique. Analytical solutions for fundamental variables such as stream function, velocity, wall shear stress, pressure gradient, and temperature are visually depicted across different physical parameter values. The findings obtained for various parameter values in the given problem demonstrate a significant influence of the amplitude ratio parameter of channel waviness, Hartmann number of the magnetic field, permeability parameter of the porous medium, Knudsen number due to the slip boundary, volume fraction of nanoparticles, radiation parameter, Prandtl number, and heat source parameters on the flow dynamics. The simulations provide valuable insights into the decrease in velocity with increasing magnetic field and its increase with increasing permeability and slip parameters. Additionally, the temperature increases with increasing nanoparticle volume fraction and radiation parameter, while it decreases with increasing Prandtl number. [ABSTRACT FROM AUTHOR]

In this paper, we consider a (ϕ 1 , ϕ 2) -Laplacian system as follows: { Δ ϕ 1 (Δ u (t − 1)) + ∇ u F (t , u (t) , v (t)) = 0 , Δ ϕ 2 (Δ v (t − 1)) + ∇ v F (t , u (t) , v (t)) = 0 , where F (t , u (t) , v (t)) = − K (t , u (t) , v (t)) + W (t , u (t) , v (t)) is T-periodic in t. By using the mountain pass theorem, we obtain that the (ϕ 1 , ϕ 2) -Laplacian system has at least one periodic solution if W is asymptotically (p , q) -linear at infinity. Our results improve and extend some known works. [ABSTRACT FROM AUTHOR]

In this paper we are concerned with an inverse problem with Robin boundary conditions, which states that, when the potential on [ 0 , 1 / 2 ] and the coefficient at the left end point are known a priori, a full spectrum uniquely determines its potential on the whole interval and the coefficient at the right end point. We shall give a new method for reconstructing the potential for this problem in terms of the Mittag-Leffler decomposition of entire functions associated with this problem. The new reconstructing method also deduces a necessary and sufficient condition for the existence issue. [ABSTRACT FROM AUTHOR]

In this paper, we prove that for certain class of initial data, the corresponding solutions to the 3-D viscous primitive equations blow up in finite time. Specifically, we find a special solution to simplify the 3-D systems, assuming that the pressure function p (x , y , t) is a concave function. We also consider the equations on the line x = 0 , y = 0 . [ABSTRACT FROM AUTHOR]

In this paper, we investigate direct and inverse problems for time-fractional pseudoparabolic equations associated with the Jacobi operator. The existence and uniqueness of the solutions are proven. Also, the stability result of the inverse source problem (ISP) is established. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence, nonexistence, and multiplicity of positive solutions to a nonlinear impulsive Sturm–Liouville boundary value problem with a parameter. By using a variational method, we prove that the problem has at least two positive solutions for the parameter λ ∈ (0 , Λ) , one positive solution for λ = Λ , and no positive solution for λ > Λ , where Λ > 0 is a constant. [ABSTRACT FROM AUTHOR]

The Kirchhoff model is derived from the vibration problem of stretchable strings. This paper focuses on the longtime dynamics of a higher-order (m 1 , m 2) -coupled Kirchhoff system with higher-order rotational inertia and nonlocal damping. We first obtain the state of the model's solutions in different spaces through prior estimation. After that, we immediately prove the existence and uniqueness of their solutions in different spaces through the Faedo-Galerkin method. Subsequently, we prove their family of global attractors using the compactness theorem. Finally, we reflect on the subsequent research of the model and point out relevant directions for further research on the model. In this way, we systematically study the longtime dynamics of the higher-order (m 1 , m 2) -coupled Kirchhoff model with higher-order rotational inertia, thus enriching the relevant findings of higher-order coupled Kirchhoff models and laying a theoretical foundation for future practical applications. [ABSTRACT FROM AUTHOR]

In the present paper, we study stochastic stability and stochastic boundedness for the stochastic differential equation (SDE) with multi-delay of third order. The derived results extend and improve some earlier results in the relevant literature, which are related to the qualitative properties of solutions to third-order delay differential equations (DDEs) and SDEs with multi-delay. Two examples are given to illustrate the results. [ABSTRACT FROM AUTHOR]

The study of multibody systems with elastic elements involves at the moment the reevaluation of the classical methods of analysis offered by analytical mechanics. Modeling this system with the finite element method requires obtaining the motion equation for an element in the circumstances imposed by a multibody system. The paper aims to present the main analysis methods used by researchers, to make a comparative analysis, and to show the advantages or disadvantages offered by different methods. For the presentation of the main methods (namely Lagrange's equations, Gibbs–Appell's equations, Maggi's formalism, Kane's equations, and Hamilton's equations) a unified notation is used. The paper provides a critical evaluation of the studied applications that involved some of these methods, highlighting the reason why it was decided to use them. Also, the paper identifies potential research areas to explore. [ABSTRACT FROM AUTHOR]

The asymptotic behavior of solutions for a new class of generalized Halanay inequalities is studied via the fixed point method. This research provides a new approach to the study of the stability of Halanay inequality. To make the application of fixed point method in stability research more flexible and feasible, we introduce corresponding functions to construct an operator according to different characteristics of coefficients. The results obtained in this paper are applied to the stability study of a neural network system, which has high value in application. Moreover, three examples and simulations are given to illustrate the results. The conclusions in this paper greatly improve and generalize the relative results in the current literature. [ABSTRACT FROM AUTHOR]

This paper is concerned with positive solutions of the limiting system arising from the Shigesada–Kawasaki–Teramoto model with large interspecific competition rate. It has previously been suggested that the limiting system has positive solutions with large amplitude for a certain value of parameters. As a first step, the purpose of this paper is to discuss the precise spatial profile of such solutions by employing formal calculations by the singular perturbation technique. [ABSTRACT FROM AUTHOR]

In this paper, we study the following chemotaxis system with a signal-dependent motility and logistic source: { u t = Δ (γ (v) u) + μ u (1 − u α) , x ∈ Ω , t > 0 , 0 = Δ v − v + u r , x ∈ Ω , t > 0 , u (x , 0) = u 0 (x) , x ∈ Ω under homogeneous Neumann boundary conditions in a smooth bounded domain Ω ⊂ R 2 , where the motility function γ (v) satisfies γ (v) ∈ C 3 ([ 0 , ∞)) with γ (v) > 0 , and | γ ′ (v) | 2 γ (v) is bounded for all v > 0 . The purpose of this paper is to prove that the model possesses globally bounded solutions. In addition, we show that all solutions (u , v) of the model will exponentially converge to the unique constant steady state (1 , 1) as t → + ∞ when μ ≥ K 4 1 + r with K = max 0 < v ≤ ∞ | γ ′ (v) | 2 γ (v) . [ABSTRACT FROM AUTHOR]

The analysis of stability in functional equations (FEs) within neutrosophic normed spaces is a significant challenge due to the inherent uncertainties and complexities involved. This paper proposes a novel approach to address this challenge, offering a comprehensive framework for investigating stability properties in such contexts. Neutrosophic normed spaces are a generalization of traditional normed spaces that incorporate neutrosophic logic. By providing a systematic methodology for addressing stability concerns in neutrosophic normed spaces, our approach facilitates enhanced understanding and control of complex systems characterized by indeterminacy and uncertainty. The primary focus of this research is to propose a novel class of Euler-Lagrange additive FE and investigate its Ulam-Hyers stability in neutrosophic normed spaces. Direct and fixed point techniques are utilized to achieve the required results. [ABSTRACT FROM AUTHOR]

The current paper concentrates on discovering the exact solutions of the time-fractional regular and singular coupled Burger's equations by involving a new technique known as the double Sumudu-generalized Laplace and Adomian decomposition method. Furthermore, some theorems of the double Sumudu-generalized Laplace properties are proved. Further, the offered method is a powerful tool for solving an enormous number of problems. The precision of the technique is evaluated with the aid of some examples, this method offers a solution precisely and successfully in a series form with smoothly calculated coefficients. The relation between both the approximate and exact solution is represented by a graph to display the high speed of this method's convergence. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of a mixed boundary value problem for a complete Sturm–Liouville equation, where the coefficients can also be negative. In particular, the existence of infinitely many distinct positive solutions to the given problem is obtained by using critical point theory. [ABSTRACT FROM AUTHOR]

The aim of this paper is to prove the existence of generalized variational solutions for nonlinear Dirichlet problems driven by anisotropic and Finsler Laplacian competing operators. The main difficulty consists in the lack of ellipticity and monotonicity in the principal part of the equations. This difficulty is overcome by developing a Galerkin-type procedure. [ABSTRACT FROM AUTHOR]

This paper solves fractional differential equations using the Shehu transform in combination with the q-homotopy analysis transform method (q-HATM). As the Shehu transform is only applicable to linear equations, q-HATM is an efficient technique for approximating solutions to nonlinear differential equations. In nonlinear systems that explain the emergence of stripes in 2D systems, the Newell–Whitehead–Segel equation plays a significant role. The findings indicate that the outcomes derived from the tables yield superior results compared to the existing LTDM in the literature. Maple is utilized to depict three-dimensional surfaces and find numerical values that are displayed in a table. [ABSTRACT FROM AUTHOR]

Over the years, the research of backward stochastic differential equations (BSDEs) has come a long way. As a extension of the BSDEs, the BSDEs with time delay have played a major role in the stochastic optimal control, financial risk, insurance management, pricing, and hedging. In this paper, we study a class of BSDEs with time-delay generators driven by Caputo fractional derivatives. In contrast to conventional BSDEs, in this class of equations, the generator is also affected by the past values of solutions. Under the Lipschitz condition and some new assumptions, we present a theorem on the existence and uniqueness of solutions. [ABSTRACT FROM AUTHOR]

In this paper, a semipositone anisotropic p-Laplacian problem − Δ p → u = λ f (u) , on a bounded domain with the Dirchlet boundary condition is considered, where A (u q − 1) ≤ f (u) ≤ B (u q − 1) for u > 0 , f (0) < 0 and f (u) = 0 for u ≤ − 1 . It is proved that there exists λ ∗ > 0 such that if λ ∈ (0 , λ ∗) , then the problem has a positive weak solution u λ ∈ L ∞ (Ω ‾) via combining Mountain-Pass arguments, comparison principles, and regularity principles. [ABSTRACT FROM AUTHOR]

This paper focuses on the long time behavior of the solutions to the Cauchy problem of the three-dimensional compressible magneto-micropolar fluids. More precisely, we aim to establish the optimal rates of temporal decay for the highest-order spatial derivatives of the global strong solutions by the method of decomposing frequency. Our result can be regarded as the further investigation of the one in (Wei, Guo and Li in J. Differ. Equ. 263:2457–2480, 2017), in which the authors only provided the optimal rates of temporal decay for the lower-order spatial derivatives of the perturbations of both the velocity and the micro-rotational velocity. [ABSTRACT FROM AUTHOR]

This paper provides a class of upper and lower solution definitions for second-order coupled systems by transforming the fourth-order differential equation into a second-order differential system. Then, by constructing a homotopy parameter and utilizing the maximum principle, we propose an upper and lower solutions method for studying a class of second-order coupled systems with Dirichlet boundary conditions and obtain an existence result. [ABSTRACT FROM AUTHOR]

In this paper, we consider a model problem arising from a classical planar Heisenberg ferromagnetic spin chain: − Δ u + V (x) u − u 1 − u 2 Δ 1 − u 2 = c | u | p − 2 u , x ∈ R N , where 2 < p < 2 ∗ , c > 0 and N ≥ 3 . By the cutoff technique, the change of variables and the L ∞ estimate, we prove that there exists c 0 > 0 , such that for any c > c 0 this problem admits a positive solution. Here, in contrast to the Morse iteration method, we construct the L ∞ estimate of the solution. In particular, we give the specific expression of c 0 . [ABSTRACT FROM AUTHOR]