Caputo-hadamard Fractional Differential Equations: Integral Boundary Condition System

Abstract

The solvability of a fractional differential equation depends on various factors such as the type of equation, the order of the fractional derivative, the domain and boundary conditions, and the properties of the solution sought. In this paper, The solution of a system of Caputo-Hadamard fractional differential equations (SCH) with integral boundary condition is investigated. The existence theorem of solutions is established by means of the Krasnoselskii and Schaefer’s fixed point theorem. Further, the uniqueness result is presented which is based on Banach’s contraction principle. Finally, the stability of the given system in Ulam-Hyers sense is applied. Examples are considered for the verification of theoretical works.