Existence Results for a Multipoint Fractional Boundary Value Problem in the Fractional Derivative Banach Space

TL;DR

This paper establishes the existence of solutions for a class of nonlinear fractional differential equations with nonlocal boundary conditions using fixed point theory in a specialized Banach space, supported by numerical examples.

Contribution

It introduces new existence results for fractional boundary value problems within a fractional derivative Banach space framework, employing Krasnosel'skii fixed point theorem.

Findings

Existence of solutions proven for nonlinear fractional differential equations.

Results demonstrated in a specific fractional derivative Banach space.

Numerical examples illustrate the theoretical findings.

Abstract

We study a class of nonlinear implicit fractional differential equations subject to nonlocal boundary conditions expressed in terms of nonlinear integro-differential equations. Using the Krasnosel'skii fixed point theorem we prove, via the Kolmogorov--Riesz criteria, existence of solutions. The existence results are established in a specific fractional derivative Banach space and they are illustrated by two numerical examples.