Existence and uniqueness of solutions for $$\Psi $$ -Caputo fractional neutral sequential differential equations on time scales

Abstract

In this paper, we establish the existence and uniqueness of solutions for a class of initial value problems involving implicit fractional differential equations with a fractional \(\Psi \)-Caputo derivative on time scales. We employ fixed point theorems by Banach, a nonlinear alternative of Leray-Schauder’s type, and Krasnoselskii’s theorem to establish these results. Finally, we present two examples to demonstrate the effectiveness of the obtained analytical results.