Existence and Ulam stability results of a coupled system for terminal value problems involving ψ-Hilfer fractional operator

Abstract

Abstract The work reported in this paper deals with the study of a coupled system for fractional terminal value problems involving ψ-Hilfer fractional derivative. The existence and uniqueness theorems to the problem at hand are investigated. Besides, the stability analysis in the Ulam–Hyers sense of a given system is studied. Our discussion is based upon known fixed point theorems of Banach and Krasnoselskii. Examples are also provided to demonstrate the applicability of our results.

Keywords

• Hilfer fractional differential equation
• Terminal value problem
• Existence and stability theory
• Fixed point theorem