Existence and Compactness Results for a System of Fractional Differential Equations

Abstract

In this work, we address the analysis of fractional differentiel equations involving the Caputo fractional derivative. By employing Perov’s fixed point theorem within the framwork of vector Banach spaces, we establish key results concerning the existence, uniqueness, boundedness, and continous dependence of solutions. Additionally, we examine the structure of the solution set, focusing on its existence, compactness, and the upper-semi-continuity of the associated solution operator.