Existence of mild solutions for Riemann-Liouville fractional differential equations with nonlocal conditions

TL;DR

This paper investigates the existence and uniqueness of mild solutions for Riemann-Liouville fractional differential equations with nonlocal conditions in Banach spaces, employing fixed point theorems and providing an illustrative example.

Contribution

It introduces new existence results for solutions of fractional differential equations with nonlocal conditions using Banach contraction and Krasnoselkii's theorems.

Findings

Existence and uniqueness of mild solutions established.

Application of Banach contraction principle and Krasnoselkii's theorem.

Illustrative example demonstrating the results.

Abstract

In this paper, we are concerned with the mild solutions of Riemann-Liouville fractional differential equations with nonlocal conditions in Banach space. We use Banach contraction principle to prove the existence and uniqueness. Moreover, we derive the existence by using Krasnoselkii's theorem. An illustrative example is presented.