Theory of Nonlinear Caputo-Katugampola Fractional Differential Equations

TL;DR

This paper studies the existence and uniqueness of solutions for fractional differential equations involving the Caputo-Katugampola derivative, using fixed point theorems and providing illustrative examples.

Contribution

It introduces new results on the solvability of Caputo-Katugampola fractional differential equations with anti-periodic boundary conditions.

Findings

Existence of solutions established under certain conditions

Uniqueness of solutions proved using fixed point theorems

Examples demonstrating the applicability of the theoretical results

Abstract

This manuscript investigates the existence and uniqueness of solutions to the first order fractional anti-periodic boundary value problem involving Caputo-Katugampola (CK) derivative. A variety of tools for analysis this paper through the integral equivalent equation of the given problem, fixed point theorems of Leray--Schauder, Krasnoselskii's, and Banach are used. Examples of the obtained results are also presented.