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The paper deals with the existence, oscillation, and nonoscillation of solutions to some classes of Caputo fractional q-difference equations and inclusions. The technique of proving employs set-valued analysis, fixed-point theory, and the method of upper and lower solutions., 1. Introduction Fractional differential equations and inclusions are applied in various areas of engineering, mathematics, physics, and other applied sciences (see [1-8], and the references therein). Recently, considerable attention has [...]

We present some results on the existence of attracting solutions of some fractional differential equations of the Hilfer type. The results on the existence of solutions are applied to the Schauder fixed-point theorem. It is proved that all solutions are uniformly locally attracting., UDC 517.9 1. Introduction Fractional differential equations have recently been applied in various areas of engineering, mathematics, physics, bioengineering, and many other applied sciences [1, 2]. For some fundamental results [...]

In this paper, we investigate the existence of asymptotically almost automorphic mild solution for a class of integro-differential equations. The existence results are established through the application of Mönch's fixed point theorem and the utilization of measures of non-compactness. Additionally, we present an illustrative example to showcase the obtained outcomes. [ABSTRACT FROM AUTHOR]

The purpose of this article is to study the existence and Ulam-Hyers stability results for a class of boundary value problems with Caputo tempered fractional derivative and infinite delay. The results are based on Monch's fixed point theorem. An illustrative example is given to demonstrate the applicability of our results. [ABSTRACT FROM AUTHOR]

Our aim in this work is to study the existence of solutions of a functional differential inclusion with finite delay. We use the Bohnenblust-Karlin fixed-point theorem for the existence of solutions., 1. Introduction In the present work, we prove the existence of solutions of a class of semilinear functional evolution inclusions with delay. Our investigations are performed in a Banach space [...]

In this paper, we prove some existence and uniqueness results for some classes of deformable implicit fractional differential equations in b-Metric spaces with initial conditions. We base our arguments on some some fixed point theorems. Finally, we provide an example to illustrate our results. [ABSTRACT FROM AUTHOR]

This paper deals with the existence and uniqueness results for a class of impulsive boundary value problem for implicit nonlinear fractional differential equations and k-Generalized ψ-Hilfer fractional derivative involving both retarded and advanced arguments. Our results are based on the Banach contraction principle and Schauder's fixed point theorem. Suitable illustrative examples are provided. [ABSTRACT FROM AUTHOR]

We first present several existence results and compactness of solutions set for the following Volterra type integral inclusions of the form: , where , is the infinitesimal generator of an integral resolvent family on a separable Banach space , and is a set-valued map. Then the Filippov's theorem and a Filippov-Ważewski result are proved.

This paper deals first with existence of bounded solutions, then followed by some oscillation results, for a coupled fractional q-difference system. For the first results, some applications are made of the fixed point theory, and the diagonalization process. Finally, we give two examples illustrating the applicability of the imposed conditions. [ABSTRACT FROM AUTHOR]

Values of λ are determined for which there exist positive solutions of the system of dynamic equations, , , for , satisfying the boundary conditions, , where is a time scale. A Guo-Krasnosel'skii fixed point-theorem is applied.

We will establish sufficient conditions for the existence of integral solutions and extremal integral solutions for semilinear functional differential equations with nondensely defined operators in Banach spaces.

The well-known Krasnoselskii twin fixed point theorem is used to investigate the existence of mild solutions for first- and second-order impulsive semilinear functional and neutral functional differential equations in Hilbert spaces.