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In this paper, Caputo boundary value problems of order 3 < ζ ≤ 4 are investigated on the interval [0, 1]. By Guo-Krasnoselskii fixed point theorem, some criteria of existence and multiplicity of positive and decreasing solutions are established. The main novelty of the paper lies in its capability to achieve positive solutions while the corresponding Green’s function changes sign. Finally, two examples are provided to illustrate the application of these results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the asymptotic stability of the trajectories governed by some delay differential inequalities on time scales. Based on time scale theory and the fixed-point theorem, some sufficient conditions are obtained for guaranteeing asymptotic stability. It is interesting that the inequalities studied in this paper include the generalized Halanay inequalities. Due to the fact that dynamic systems on a time scale unify discrete and continuous systems, the results of this paper have wider application value. Furthermore, some numerical examples verify the main results. [ABSTRACT FROM AUTHOR]

This research paper presented a novel investigation into an implicit coupled system of fractional variable order, which has not been previously studied in the existing literature. The study focused on establishing and developing sufficient conditions for the existence and uniqueness of solutions, as well as the Ulam-Hyers stability, for the proposed coupled system without using semigroup property. By extending the existing conclusions examined for the Atangana-Baleanu-Caputo (ABC) operator, we contributed to advancing the understanding of variable-order fractional differential equations. The paper provided a solid theoretical foundation for further analysis, numerical simulations, and practical applications. The obtained results have implications for designing and controlling systems modeled using fractional variable order equations and serve as a basis for addressing a wide range of dynamical problems. The transformation techniques, qualitative analysis, and illustrative examples presented in this work highlight its unique contributions and potential to serve as a foundation for future research. [ABSTRACT FROM AUTHOR]

This paper aims to investigate the existence, uniqueness, and stability properties for a class of fractional weighted Cauchy-type problem in the variable exponent Lebesgue space Lp(.). The obtained results are set up by employing generalized intervals and piece-wise constant functions so that the Lp(.) is transformed into the classical Lebesgue spaces. Moreover, the usual Banach Contraction Principle is utilized, and the Ulam-Hyers (UH) stability is studied. At the final stage, we provide an example to support the accuracy of the obtained results. [ABSTRACT FROM AUTHOR]

This paper aims to investigate a class for nonlocal fractional boundary value problem on an infinite interval due to its importance in provide a powerful tool for mathematical modeling of complex phenomena in science. New existence results are acquired for the given problem by using the Krasnosel'skii's fixed point theorem. Moreover, sufficient conditions are obtained as well as a modified compactness criterion that guarantees the existence of at least one solution. In addition, an illustrative example is given in the final part of the paper. [ABSTRACT FROM AUTHOR]

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In this paper we prove the existence of solutions for fractional order functional and neutral functional differential equations with infinite delay principles combined with a technique based on vector-valued metrics and convergent to zero matrices. [ABSTRACT FROM AUTHOR]

In this paper, we present a result on the existence of asymptotically stable solutions of infinite systems (IS) of quadratic Hammerstein integral equations (IEs). Our study will be conducted in the Banach space of functions, which are continuous and bounded on the half-real axis with values in the classical Banach sequence space consisting of real bounded sequences. The main tool used in our investigations is the technique associated with the measures of noncompactness (MNCs) and a fixed point theorem of Darbo type. The applicability of our result is illustrated by a suitable example at the end of the paper. [ABSTRACT FROM AUTHOR]

In this paper, we study a quantum difference coupled impulsive system with respect to another function. Some quantum derivative and integral asymmetric graphs with respect to another function are shown to illustrate the behavior of parameters. Existence and uniqueness results are established via Banach contraction mapping principle and Leray–Schauder alternative. Examples illustrating the obtained results are also included. Our results are new and significantly contribute to the literature to this new subject on quantum calculus on finite intervals with respect to another function. [ABSTRACT FROM AUTHOR]

The paper investigated the exact controllability of delayed fractional evolution systems of order α ∈ (1, 2) in abstract spaces. At first, the exact controllability result is obtained when the nonlinear term f is locally Lipschitz continuous. Then, the certain compactness conditions and the measure of noncompactness conditions were applied to demonstrate the exact controllability of the concerned problem. The discussion was based on the fixed point theorems and the cosine family theory. [ABSTRACT FROM AUTHOR]

The primary focus of this paper is threefold: first, to investigate the existence of mild solutions; second, to analyze the topological and geometrical structure of the solution sets; and third, to determine the continuous dependence of the solution for second-order semilinear integro-differential inclusion. In this study, we employ Bohnenblust–Karlin’s fixed point theorem in conjunction with the theory of resolvent operators, as presented by Grimmer. An illustrative example is employed to showcase the achieved outcomes. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to study the Cauchy problem for nonlinear differential equations of fractional order containing the weighted Riemann-Liouville fractional derivative of a function with respect to another function. The equivalence of this problem and a nonlinear Volterratype integral equation of the second kind have been presented. In addition, the existence and uniqueness of the solution to the considered Cauchy problem are proved using Banach's fixed point theorem and the method of successive approximations. Finally, we obtain a new estimate of the weighted Riemann-Liouville fractional derivative of a function with respect to functions at their extreme points. With the assistance of the estimate obtained, we develop the comparison theorems of fractional differential inequalities, strict as well as nonstrict, involving weighted Riemann-Liouville differential operators of a function with respect to functions of order d, 0 < d < 1. [ABSTRACT FROM AUTHOR]

This paper investigates the existence and uniqueness of solutions for a system of Hilfer-Hadamard sequential fractional differential equations using standard fixed-point theorems. We apply the Leray-Schauder alternative and Banach's contraction mapping principle to obtain the existence and uniqueness results for the given problem. Additionally, we discuss illustrative examples. [ABSTRACT FROM AUTHOR]

In this paper, we use a novel approach to study the existence, uniqueness, and stability of solutions (EUSS) to a Cauchy-type problem of nonlinear fractional differential equations (FrDiEq) of variable order with infinite delay (CPNFDEVOID). Contrary to the techniques taken in the literature, which were centered on the usage of the concept of generalized intervals and the idea of piecewise constant functions, our approach is straightforward and based on a novel fractional operator that is more appropriate and demonstrates the solvability and stability of the main problem under less restrictive presumptions. The results are achieved in this paper by using Fixed Point Theory (FPT). The application, which includes an example and supporting images, concludes the paper. [ABSTRACT FROM AUTHOR]

In this paper, we studied the generalizations of quantum calculus on finite intervals. We presented the new definitions of the quantum derivative and quantum integral of a function with respect to another function and studied their basic properties. We gave an application of these newly defined quantum calculi by obtaining a new Hermite-Hadamard inequality for a convex function. Moreover, an impulsive boundary value problem involving quantum derivative, with respect to another function, was studied via the Banach contraction mapping principle. [ABSTRACT FROM AUTHOR]

In this paper, we explore the stability of a new class of Caputo-type fractional stochastic delay differential systems with Poisson jumps. We prove the Hyers–Ulam stability of the solution by utilizing a version of fixed point theorem, fractional calculus, Cauchy–Schwartz inequality, Jensen inequality, and some stochastic analysis techniques. Finally, an example is provided to illustrate the effectiveness of the results. [ABSTRACT FROM AUTHOR]

Monge–Ampère equations have important research significance in many fields such as geometry, convex geometry and mathematical physics. In this paper, under some superlinear and sublinear conditions, the existence of nontrivial solutions for a system arising from Monge–Ampère equations with two parameters is investigated based on the Guo–Krasnosel'skii fixed point theorem. In the end, two examples are given to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we consider the existence of positive solutions for a system of fractional q -difference equations with generalized p -Laplacian operators. By using Guo-Krasnosel'skii fixed point theorem, we obtain some existence results of positive solutions for this system with two parameters under some different combinations of superlinearity and sublinearity of the nonlinear terms. In the end, we give two examples to illustrate our main results. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence and uniqueness of a positive solution for a boundary value problem of nonlinear fractional integro-differential equations involving a generalized version of the Riemann–Liouville fractional derivative with respect to another function ψ and integral boundary conditions. Using the Banach's contraction principle and Schaefer's fixed point theorem together with the upper and lower solution method we prove our main results. Finally, an example is presented to illuminate our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the existence of the solutions of a class of weakly singular integral equations in Banach algebra is investigated. The basic tool used in investigations is the technique of the measure of non-compactness and Petryshyn's fixed point theorem. Also, for the applicability of the obtained results, some examples are given. [ABSTRACT FROM AUTHOR]

In this paper, we study a matrix equation involving the matrix geometric mean . We study several properties and inequalities for the unique solution of such an equation. We also use the weighted geometric mean to define a new quantum Hellinger divergence and show that the new quantum divergence satisfies the Data Processing Inequality. [ABSTRACT FROM AUTHOR]

In this paper, we present a new fixed-point result to draw conclusions about the existence and uniqueness of the solution for a nonlinear Fredholm integral equation of the second kind with non-differentiable Nemytskii operator. To do this, we will transform the problem of locating a fixed point for an integral operator into the problem of locating a solution of an integral equation. Thus, assuming conditions on the Nemytskii operator, we will obtain a global convergence domain for the solution of the considered integral equation, taking for this a uniparametric family of derivativefree iterative processes with quadratic convergence. This result provides us a new fixed-point result for the integral operator considered. [ABSTRACT FROM AUTHOR]

In the present paper, we mainly focus on an iterative erythropoiesis model with a nonlinear harvesting term involving a time-varying delay. Under certain conditions and by the Schauder fixed point theorem, we show that the existence of positive periodic solutions can be guaranteed and based on the Banach fixed point theorem, we establish the existence as well as the continuous dependence on parameters theorems of the unique solution. Moreover, two examples are provided to validate the correctness of our outcomes. Our theoretical findings extend and improve several related ones in the existing literature. [ABSTRACT FROM AUTHOR]

In this paper, we study the main results of existence and uniqueness of mild solutions of fractional Volterra integrodifferential equation involving Caputo fractional derivative of special class n - 1 < α ≤ n, n > 1. Furthermore, the various type of dependency of mild solutions of the proposed problem have been studied such as dependence on given initial data, continuously depends on the functions involved in the right side of the problem and on real parameters. The result of existence and uniqueness is obtained with help of well known Banach contraction principle and the integral inequality established by B. G. Pachpatte which provides explicit bound on the unknown function. A suitable example is given to demonstrate the obtained results. [ABSTRACT FROM AUTHOR]

Summary In this paper, computational analysis of a Caputo fractional variable‐order system with inductor‐capacitor (LC) and resistor‐capacitor (RC) electrical circuit models is presented. The existence and uniqueness of solutions to the given problem are determined using Schaefer's fixed point theorem and the Banach contraction principle, respectively. The proposed problem's computational consequences are addressed and analyzed using modified Euler and Runge–Kutta fourth‐order techniques. Furthermore, the suggested model compares several orders, including integer, fractional, and variable orders. To demonstrate the utility of the proposed approach, computational simulations are carried out on LC and RC circuit models of various orders. Furthermore, a comparative analysis with previous investigations has been carried. For the given problem, the numerical solution results in high‐precision approximations. [ABSTRACT FROM AUTHOR]

This paper is concerned with nonhomogenous Choquard equations involving doubly critical exponents. First, we use a fixed point theorem to prove the existence of positive solutions to the above equation under certain assumptions. Then, on the positive solution of the equation, we get the regularity in a bounded domain with estimating the L∞$$ {L}&#x0005E;{\infty } $$‐bounds by Moser's iterative technique. [ABSTRACT FROM AUTHOR]

In this paper, we provide existence results to the following boundary value problem {−u' = q(t)f(t, u(t), u' (t)), t ∈ (0, +∞), u(0) = 0, u' (∞)=0, where q ∈ L¹((0, +∞), R) and the nonlinearity f: [0, +∞[×R × R → R is continuous. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the (μ 1 , μ 2) -pseudo-asymptotically τ -periodicity and its applications. Then, the problems of existence, uniqueness and global exponential stability of (μ 1 , μ 2) -pseudo-asymptotically τ -periodic solutions for neural networks with delay are considered. Finally, three examples are given to illustrate the validity of the theoretical results [ABSTRACT FROM AUTHOR]

Purpose – This paper aims to study qualitative properties and approximate solutions of a thermostat dynamics system with three-point boundary value conditions involving a nonsingular kernel operator which is called Atangana-Baleanu-Caputo (ABC) derivative for the first time. The results of the existence and uniqueness of the solution for such a system are investigated with minimum hypotheses by employing Banach and Schauder's fixed point theorems. Furthermore, Ulam-Hyers (UH) stability, Ulam-Hyers-Rassias UHR stability and their generalizations are discussed by using some topics concerning the nonlinear functional analysis. An efficiency of Adomian decomposition method (ADM) is established in order to estimate approximate solutions of our problem and convergence theorem is proved. Finally, four examples are exhibited to illustrate the validity of the theoretical and numerical results. Design/methodology/approach – This paper considered theoretical and numerical methodologies. Findings – This paper contains the following findings: (1) Thermostat fractional dynamics system is studied under ABC operator. (2) Qualitative properties such as existence, uniqueness and Ulam–Hyers–Rassias stability are established by fixed point theorems and nonlinear analysis topics. (3) Approximate solution of the problem is investigated by Adomain decomposition method. (4) Convergence analysis of ADM is proved. (5) Examples are provided to illustrate theoretical and numerical results. (6) Numerical results are compared with exact solution in tables and figures. Originality/value – The novelty and contributions of this paper is to use a nonsingular kernel operator for the first time in order to study the qualitative properties and approximate solution of a thermostat dynamics system.

This research paper presented a novel investigation into an implicit coupled system of fractional variable order, which has not been previously studied in the existing literature. The study focused on establishing and developing sufficient conditions for the existence and uniqueness of solutions, as well as the Ulam-Hyers stability, for the proposed coupled system without using semigroup property. By extending the existing conclusions examined for the Atangana-Baleanu-Caputo (ABC) operator, we contributed to advancing the understanding of variable-order fractional differential equations. The paper provided a solid theoretical foundation for further analysis, numerical simulations, and practical applications. The obtained results have implications for designing and controlling systems modeled using fractional variable order equations and serve as a basis for addressing a wide range of dynamical problems. The transformation techniques, qualitative analysis, and illustrative examples presented in this work highlight its unique contributions and potential to serve as a foundation for future research.

This paper focuses on revisiting and improving the results regarding the existence of a solution to the implicit fractional differential equations (FDEs) given in the following form: DCρω(ϰ)=fϰ,ω(ϰ),DCρω(ϰ)$$ {\mathcal{D}}_C&#x0005E;{\rho}\omega \left(\mathrm{\varkappa}\right)&#x0003D;f\left(\mathrm{\varkappa},\omega \left(\mathrm{\varkappa}\right),{\mathcal{D}}_C&#x0005E;{\rho}\omega \left(\mathrm{\varkappa}\right)\right) $$for all ϰ∈[0,T]$$ \mathrm{\varkappa}\in \left[0,T\right] $$ with the initial condition ω(0)=ω0$$ \omega (0)&#x0003D;{\omega}_0 $$, where 0<ρ<1,DCρ$$ 0<\rho <1,{\mathcal{D}}_C&#x0005E;{\rho } $$ is the Caputo fractional derivative (CFD). Mainly, we aim to weaken the necessary conditions often found in the literature for guaranteeing the existence of solution. [ABSTRACT FROM AUTHOR]

A mathematical model of progressive disease of the nervous system also called multiple sclerosis (MS) is studied in this paper. The proposed model is investigated under the concept of the fractal-fractional order derivative (FFOD) in the Caputo sense. In addition, the tools of nonlinear functional analysis are applied to prove some qualitative results including the existence theory, stability, and numerical analysis. For the recommended results of the existence theory, Banach and Krassnoselski's fixed point theorems are used. Additionally, Hyers–Ulam (HU) concept is used to derive some results for stability analysis. Additionally, for numerical illustration of approximate solutions of various compartments of the considered model, the modified Euler method is utilized. The aforementioned results are displayed graphically for various values of fractal-fractional orders. [ABSTRACT FROM AUTHOR]

The goal of this paper is to establish a general fixed point theorem for compact single-valued continuous mappings in Hausdorff p-vector spaces, and a fixed point theorem for upper semicontinuous set-valued mappings in locally p-convex spaces for p 2 (0; 1]. These results not only provide a solution to Schauder conjecture in the affirmative under the setting of p-vector spaces for compact single-valued continuous mappings, but also show the existence of fixed points for upper semicontinuous set-valued mappings defined on s-convex subsets in Hausdorff locally p-convex spaces, which would be fundamental for nonlinear functional analysis, where s; p 2 (0; 1]. [ABSTRACT FROM AUTHOR]

In this paper, the solvability of an infinite system of integral equations of the Volterra--Hammerstein type in Banach space BC(R+ + R+,c0) is examined. Technique associated with the measure of noncompactness plays the most important role in adopted analysis and authors present an example to validate the applicability of the result. [ABSTRACT FROM AUTHOR]

The partial neutral functional fractional differential equation described by the fractional operator is considered in the present investigation. The used fractional operator is the Caputo derivative. In the present paper, the fractional resolvent operators have been defined and used to prove the existence of the unique solution of the fractional neutral differential equations. The fixed point theorem has been used in existence investigations. For an illustration of our results in this paper, an example has been provided as well.

The main purpose of this paper is to examine the inverse problem associated with determining the right-hand side of a nonlinear fractional parabolic equation. This equation is accompanied by an integral over-determination supplementary condition. With the use of the functional analysis method, we establish the continuity, existence and uniqueness based on the construction of the direct problem. Such a method relies on the density of the range of the operator established for the problem at hand coupled with the energy inequality scheme. This scheme, also referred to as the method of a priori estimates, allows us to derive the existence theorem from the solution of the given problem, starting with the uniqueness theorem. For the solvability of the inverse problem and its uniqueness, we establish certain suitable conditions, and to demonstrate the existence and uniqueness of its solution, we utilize the fixed point theorem. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence and regularity results for some parabolic equations with degenerate coercivity, and a singular right-hand side. The model problem is 0.1 { ∂ u ∂ t − div ( (1 + | ∇ u | − Λ) | ∇ u | p − 2 ∇ u (1 + | u |) θ) = f (e u − 1) γ in Q T , u (x , 0) = 0 on Ω , u = 0 on ∂ Q T , where Ω is a bounded open subset of R N N ≥ 2 , T > 0 , Λ ∈ [ 0 , p − 1) , f is a non-negative function belonging to L m (Q T) , Q T = Ω × (0 , T) , ∂ Q T = ∂ Ω × (0 , T) , 0 ≤ θ < p − 1 + p N + γ (1 + p N) and 0 ≤ γ < p − 1 . [ABSTRACT FROM AUTHOR]