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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]

This paper focuses on using piecewise derivatives to simulate the dynamic behavior and investigate the crossover effect within the coupled fractional system with delays by dividing the study interval into two subintervals. We establish and prove significant lemmas concerning piecewise derivatives. Furthermore, we extend and develop the necessary conditions for the existence and uniqueness of solutions, while also investigating the Hyers–Ulam stability results of the proposed system. The results are derived using the Banach contraction principle and the Leary–Schauder alternative fixed-point theorem. Additionally, we employ a numerical method based on Newton’s interpolation polynomials to compute approximate solutions for the considered system. Finally, we provide an illustrative example demonstrating our theoretical conclusions’ practical application. [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]

In this paper, we introduce new types of contraction mappings named S-Pata-type contraction mapping and Generalized S-Pata-type contraction mapping in the framework of S-metric space. Then, we prove some new fixed-point results for S-Pata-type contraction mappings and Generalized S-Pata-type contraction mappings. To support our results, we provide examples to illustrate our findings and also apply these results to the ordinary differential equation to strengthen our conclusions. [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]

Recent research indicates the need for improved models of physical phenomena with multiple shocks. One of the newest methods is to use differential inclusions instead of differential equations. In this work, we intend to investigate the existence of solutions for an m-dimensional system of quantum differential inclusions. To ensure the existence of the solution of inclusions, researchers typically rely on the Arzela–Ascoli and Nadler's fixed point theorems. However, we have taken a different approach and utilized the endpoint technique of the fixed point theory to guarantee the solution's existence. This sets us apart from other researchers who have used different methods. For a better understanding of the issue and validation of the results, we presented numerical algorithms, tables, and some figures. The paper ends with an example. [ABSTRACT FROM AUTHOR]

This paper deals with a class of second-order linear differential equations with periodic coefficients. By viable transformation, we put the second-order linear differential equation into Riccati’s equation. By means of two periodic solutions of Riccati’s equation and variable transformation, we obtain the existence and uniqueness of the periodic solution of the nonhomogeneous second-order linear differential equation, some new results are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of generalized (α , ϕ) -Meir–Keeler hybrid contractive mappings of type I and II via simulation function and establish fixed point theorems for such mappings in the setting of complete b-metric spaces. Our results extend and generalize many related fixed point results in the existing literature. Finally, we provide an example in support of our main finding. [ABSTRACT FROM AUTHOR]

We provide in this paper a numerical iterative approach for solving nonlinear fuzzy integral equations using Newton–Cotes rules (abbreviated NC rules). We show how to employ NC rules and successive approximation sequences to approximate the Urysohn fuzzy integral equation of the second kind. The modulus of continuity will be utilized for demonstrating convergence analysis and error estimation. Finally, we evaluate the efficiency, accuracy, and applicability of theoretical conclusions of our technique in practice examples from reliable references. The errors demonstrate the method's excellent accuracy. [ABSTRACT FROM AUTHOR]

The study of the zero existence problem for a nonnegative set-valued functional on a metric space is continued. The zero existence problem for a functional related by a certain -continuity condition to a parametric family of -search functionals on an open subset of a metric space is examined. A theorem containing several sufficient conditions for this functional to have zeros is proved. As corollaries of this result, theorems on the existence of coincidence and fixed points are also proved for set-valued mappings related by the -continuity condition to families of set-valued mappings with the property that the existence of coincidence and fixed points in an open subset of a metric space is preserved under parameter variation. For uniformly convex metric spaces, analogs of M. Edelstein's 1972 asymptotic center theorem and M. Frigon's 1996 fixed point theorem for nonexpansive mappings of Banach spaces are obtained and compared with the main results of the paper. [ABSTRACT FROM AUTHOR]

This paper is the first to introduce a fixed point problem of integral type in a -metric space. We study sufficient conditions for the existence and uniqueness of a common fixed point of contractive mappings of integral type. We also give two examples to support our results. [ABSTRACT FROM AUTHOR]

A general fixed point theorem for isometries in terms of metric functionals is proved under the assumption of the existence of a conical bicombing. It is new for isometries of convex sets of Banach spaces as well as for non-locally compact CAT(0)-spaces and injective spaces. Examples of actions on non-proper CAT(0)-spaces come from the study of diffeomorphism groups, birational transformations, and compact Kähler manifolds. A special case of the fixed point theorem provides a novel mean ergodic theorem that in the Hilbert space case implies von Neumann's theorem. The theorem accommodates classically fixed-point-free isometric maps such as those of Kakutani, Edelstein, Alspach and Prus. Moreover, from the main theorem together with some geometric arguments of independent interest, one can deduce that every bounded invertible operator of a Hilbert space admits a nontrivial invariant metric functional on the space of positive operators. This is a result in the direction of the invariant subspace problem although its full meaning is dependent on a future determination of such metric functionals. [ABSTRACT FROM AUTHOR]

Purpose: This paper propose a grounded-type DVA attached to a damped primary system, which can effectively suppress the vibration amplitudes by introducing a lever, focusing on the optimal design of the novel DVA. It can be utilized to the simplified model of a damped spacecraft or stay cable of cable-stayed bridges. Methods: The design of DVA considers H ∞ and H 2 optimization criteria, and defines performance indicators separately. In the H ∞ optimization, we couple generalized fixed-point theory (GFPT) and perturbation method (PM) with particle swarm optimization (PSO) algorithm to minimize the maximum amplitude amplification factor of primary system, so that the amplitudes at two fixed points are close to the same horizontal line. Nevertheless, in the H 2 optimization, the GFPT and PM are combined with Newton's method to minimize the power input to primary system. Results: The numerical results indicate the consistency and effectiveness of the two optimization criteria. Compared with other classical models, the effects of different grounded stiffness ratios on the amplitude frequency responses, time histories, and vibration energies of the primary system subjected to harmonic excitation and random excitation, respectively, as well as the vibration reduction effect, are studied. Conclusions: Numerical simulations display with the positive grounded stiffness, the proposed DVA outperform the existing DVAs with same mass, damping, and stiffness under the harmonic excitation and random excitation. The results can provide theoretical and computational guidance for the optimal design of DVA. [ABSTRACT FROM AUTHOR]

The contraction condition in the Banach contraction principle forces a function to be continuous. Many authors overcome this obligation and weaken the hypotheses via metric spaces endowed with a partial order. In this paper, we present some coupled fixed point theorems for the functions having mixed monotone properties on ordered vector metric spaces, which are more general spaces than partially ordered metric spaces. We also define the double monotone property and investigate the previous results with this property. In the last section, we prove the uniqueness of a coupled fixed point for non-monotone functions. In addition, we present some illustrative examples to emphasize that our results are more general than the ones in the literature. [ABSTRACT FROM AUTHOR]

This paper investigates on the H ∞ and H 2 control performances for a novel grounded inerter-based dynamic vibration absorber configuration (GIDVA) by entirely replacing both damper and stiffness of the classic dynamic vibration absorber with grounded inerter-based mechanical network. First, the equations of motion of the coupled system are derived and the analytical solution is established in terms of primary system displacement under harmonic excitation. Then, the optimum tuning parameters are found by first using the extended fixed points theory (EFPT) to get analytical design. It is found that this EFPT yields the approximate but accurate analytical solutions, so this method can be commonly used to design inerter-based DVAs with four fixed points in the frequency response curves of the primary system. Further, to evaluate the control performance of the proposed GIDVA, the numerical H ∞ and H 2 optimizations are performed in MATLAB for the case of harmonic and random excitation, respectively, using the Newton–Raphson algorithm with the starting points, the analytical approximate optimal parameters based on the EFPT. Based on the results comparison of the control performance, one can remark that with the same small mass ratio, the proposed GIDVA can decrease the peak vibration amplitude of primary system more than 64% and 50% and enlarge the suppression bandwidth more than 64% and 57% when compared with the classic DVA and the recent published non-traditional inerter-based DVAs (NIDVA- C i , i=3, 4, 6), respectively, for both optimal designs H ∞ and H 2 . However, one can also notice that this improvement decreases with the increase in the mass ratio. Moreover, under random excitation, the GIDVA also shows good control performance with 56% and 44% reduction in terms of mean square and time history responses of primary system. This result reveals the potential of a novel grounded inerter-based dynamic vibration absorber, which provides a reference for the design index of the novel vibration absorber in engineering practice. [ABSTRACT FROM AUTHOR]

The survey of the available literature shows that a lot of important invariant point problems of Banach and Heilpern types have been examined in both metric and quasimetric spaces. However, a handful of the existing results employed the recent approaches of interpolative contractions. Therefore, based on the new idea of interpolation techniques in fixed point theory, this article studies new notions of L-fuzzy contractions and investigates conditions for the existence of L-fuzzy fixed points for such mappings. On the fact that fixed points of point-to-point mappings satisfying interpolative-type contraction are not always unique, whence making the concepts more fitted for invariant point results of crisp set-valued maps, new multi-valued analogues of the key findings put forward in this work are derived. Comparative illustrations, which indicate the preeminence of the results presented herein, are constructed. From application viewpoint, one of the theorems so obtained is employed to introduce new solvability conditions of Fredholm-type integral inclusions. [ABSTRACT FROM AUTHOR]

A comprehensive mathematical model is proposed to study two strains of dengue virus with saturated incidence rates and quarantine measures. Imperfect dengue vaccination is also assumed in the model. Existence, uniqueness and stability of the proposed model are proved using the results from fixed point and degree theory. Additionally, well constructed Lyapunov function candidates are also applied to prove the global stability of infection-free equilibria. It is also demonstrated that the model is generalized Ulam-Hyers stable under some appropriate conditions. The model is fitted to the real data of dengue epidemic taken from the city of Espirito Santo in Brazil. For the approximate solution of the model, a non-standard finite difference(NSFD) approach is applied. Sensitivity analysis is also carried out to show the influence of different parameters involved in the model. The behaviour of the NSFD is also assessed under different denominator functions and it is observed that the choice of the denominator function could influence the solution trajectories. Different scenario analysis are also assessed when the reproduction number is below or above one. Furthermore, simulations are also presented to assess the epidemiological impact of dengue vaccination and quarantine measures for infected individuals. [ABSTRACT FROM AUTHOR]

This article investigates sufficient conditions for the existence and uniqueness of solutions to the ψ-Hilfer sequential type pantograph fractional boundary value problem. Considering the system depends on a lower-order fractional derivative of an unknown function, the study is carried out in a special working space. Standard fixed point theorems such as the Banach contraction principle and Krasnosel'skii's fixed point theorem are applied to prove the uniqueness and the existence of a solution, respectively. Finally, an example demonstrating our results with numerical simulations is presented. [ABSTRACT FROM AUTHOR]

In this study, we manifest a new class of mappings that satisfy Geraghty–Ćirić-type contractive conditions in the context of b-metric spaces and prove a theorem on the existence and uniqueness of fixed points. Our results unify and generalize the results of Geraghty; Ćirić; Dukic, Kadelburg, and Radenović; and Shu-fang Li, Fei Hi, and Ning Lu in the setting of b-metric spaces. Furthermore, we provide examples to verify the correctness and applicability of our results. We also utilize our findings to show the existence of a unique solution for a nonlinear integral equation. [ABSTRACT FROM AUTHOR]

The objective of this research is to present new fixed point theorems for two separate families of fuzzy-dominated mappings. These mappings must satisfy a unique locally contraction in a complete b-multiplicative metric space. Also, we have obtained novel results for families of fuzzy-dominated mappings on a closed ball that meet the requirements of a generalized locally contraction. This research introduces new and challenging fixed-point problems for families of ordered fuzzy-dominated mappings in ordered complete b-multiplicative metric spaces. Moreover, we demonstrate a new concept for families of fuzzy graph-dominated mappings on a closed ball in these spaces. Additionally, we present novel findings for graphic contraction endowed with graphic structure. These findings are groundbreaking and provide a strong foundation for future research in this field. To demonstrate the uniqueness of our novel findings, we provide evidence of their applicability in obtaining the common solution of integral and fractional differential equations. Our findings have resulted in modifications to several contemporary and classical results in the research literature. This provides further evidence of the originality and impact of our work. [ABSTRACT FROM AUTHOR]

We set up a unified framework to efficiently compute the shear and bulk viscosities of strongly coupled gauge theories with gravitational holographic duals involving higher derivative corrections. We consider both Weyl4 corrections, encoding the finite 't Hooft coupling corrections of the boundary theory, and Riemann2 corrections, responsible for non-equal central charges c ≠ a of the theory at the ultraviolet fixed point. Our expressions for the viscosities in higher derivative holographic models are extracted from a radially conserved current and depend only on the horizon data. [ABSTRACT FROM AUTHOR]

This manuscript aims to present new results about the generalized F-contraction of Hardy–Rogers-type mappings in a complete vector-valued metric space, and to demonstrate the fixed-point theorems for single and pairs of generalized F-contractions of Hardy–Rogers-type mappings. The established results represent a significant development of numerous previously published findings and results in the existing body of literature. Furthermore, to ensure the practicality and effectiveness of our findings across other fields, we provide an application that demonstrates a unique solution for the semilinear operator system within the Banach space. [ABSTRACT FROM AUTHOR]

The present research is aimed to analyze the existence of strict fixed points (SFPs) and fixed points of multivalued generalized contractions on the platform of controlled metric spaces (CMSs). Wardowski-type multivalued nonlinear operators have been introduced employing auxiliary functions, modifying a new contractive requirement form. Well-posedness of obtained fixed point results is also established. Moreover, data dependence result for fixed points is provided. Some supporting examples are also available for better perception. Many existing results in the literature are particular cases of the results established. [ABSTRACT FROM AUTHOR]

In this article, we analyze the existence, multiplicity and nonexistence of positive solutions for a class of biharmonic equations with Navier boundary conditions and a parameter. In addition, some new criteria for the existence, multiplicity and nonexistence of positive radial solutions for a singular biharmonic equation are also investigated. Our approaches use fixed point theorems on cones. [ABSTRACT FROM AUTHOR]

In this manuscript, we use the concept of multidimensional fixed point in a generalized space, namely, C-distance space with some nonlinear contraction conditions, such as Jaggi- and Dass-Gupta-type contractions. We provide results with a Jaggi-type hybrid contraction for the mentioned space. Moreover, we use control functions to get the desired results. After each theorem, we compare our results with previous ones to show that they are generalized. We provide examples to support our results. An application is also performed to solve the system of integral equations. [ABSTRACT FROM AUTHOR]

This study focuses on improving the accuracy of assessing liver damage and early detection for improved treatment strategies. In this study, we examine the human liver using a modified Atangana-Baleanu fractional derivative based on the mathematical model to understand and predict the behavior of the human liver. The iteration method and fixed-point theory are used to investigate the presence of a unique solution in the new model. Furthermore, the homotopy analysis transform method, whose convergence is also examined, implements the mathematical model. Finally, numerical testing is performed to demonstrate the findings better. According to real clinical data comparison, the new fractional model outperforms the classical integer-order model with coherent temporal derivatives. [ABSTRACT FROM AUTHOR]