Existence Results for Coupled Implicit \({\psi}\)-Riemann–Liouville Fractional Differential Equations with Nonlocal Conditions

Abstract

In this paper, we study the existence and uniqueness of solutions for a coupled implicit system involving ψ-Riemann–Liouville fractional derivative with nonlocal conditions. We first transformed the coupled implicit problem into an integral system and then analyzed the uniqueness and existence of this integral system by means of Banach fixed-point theorem and Krasnoselskiis fixed-point theorem. Some known results in the literature are extended. Finally, an example is given to illustrate our theoretical result.

Averaging Principle for ψ-Capuo Fractional Stochastic Delay Differential Equations with Poisson Jumps

“…In [28], Almeida generalized the definition of the Caputo fractional derivative by considering the Caputo fractional derivative of a function with respect to another function ψ. Since then, there have been so many papers involving the ψ-Caputo fractional derivative, see [29][30][31][32]. Recently, there have been many works on SDEs with Poisson jumps, see, for example, [33][34][35] and the references therein.…”