In this paper, we introduce and study a new class of boundary value problems, consisting mixed-type ?1-Hilfer ?2-Caputo fractional order differential equation supplemented with integro-differential nonlocal conditions. The uniqueness solutions is achieved via the Banach contraction principle, while existence results established by using Leray–Schauder nonlinear alternative. Numerical examples a...

In this paper, we prove some new fixed point theorems involving set-valued F-contractions in the setting of quasi-ordered metric spaces. Our results are significant since present Banach contraction principle a different manner from that which is known literature. Some examples and an application to existence solution Volterra-type integral equation given support obtained

In this paper, the Ulam stability of an n-th order delay integro-differential equation is given. Firstly, existence and uniqueness theorem a solution for obtained using Lipschitz condition Banach contraction principle. Then, expression derived by mathematical induction. On basis, we obtain via Gronwall–Bellman inequality. Finally, two examples equations are given to explain our main results.

Abstract In this paper, we mainly study a kind of fractional-order multiple point boundary value problem involving noninstantaneous impulse and abstract bounded operator. The existence uniqueness is obtained by the Banach contraction principle. And applying direct analysis methods, establish some conditions Ulam–Hyers stability for problem. Finally, an interesting application example given to i...

Abstract In the current manuscript, we combine q -fractional integral operator and derivative to investigate a coupled hybrid fractional -differential systems with sequential -derivatives. The existence uniqueness of solutions for proposed system are established by means Leray-Schauder’s alternative Banach contraction principle. Furthermore, Ulam-Hyers Ulam-Hyers-Rassias stability results discu...

Abstract We investigate the existence and uniqueness of solutions to a coupled system hybrid fractional integro-differential equations involving ? -Caputo operators. To achieve this goal, we make use fixed point theorem for sum three operators due Dhage also result is obtained by making Banach contraction principle. Moreover, explore Ulam–Hyers stability its generalized version given system. An...

This paper is concerned with the existence and uniqueness of solutions for a new class boundary value problems, consisting by Hilfer-Hadamard fractional differential equations, supplemented nonlocal integro-multipoint conditions. The unique solution obtained via Banach contraction mapping principle, while results are established applying Schaefer Krasnoselskii fixed point theorems as well Leray...

This paper considers boundary value problem (BVP) for nonlinear first-order differential problems with multipoint and integral conditions. A suitable Green function was constructed the first time in order to reduce this into a corresponding equation. So that by using Banach contraction mapping principle (BCMP) Schaefer’s fixed point theorem (SFPT) on equation, we can show solution of exists it ...

In this paper, we focus on the study of implicit FDE involving Stieltjes integral boundary conditions. We first exploit some sufficient conditions to guarantee existence and uniqueness solutions for above problems based Banach contraction principle Schaefer’s fixed point theorem. Then, present different kinds stability such as UHS, GUHS, UHRS, GUHRS by employing classical techniques. end, main ...

This article outlines the necessary requirements for a coupled system of fractional order boundary value involving Caputo derivative, including its existence, uniqueness, and various forms Ulam stability. We demonstrate existence uniqueness proposed by using cone-type Leray–Schauder result Banach contraction principle. Based on traditional method nonlinear functional analysis, stability is exam...