Neutral functional sequential differential equations with Caputo fractional derivative on time scales

Abstract

Abstract In this paper, we establish the existence and uniqueness of a solution for a class of initial value problems for implicit fractional differential equations with Caputo fractional derivative. The arguments are based upon the Banach contraction principle, the nonlinear alternative of Leray–Schauder type and Krasnoselskii fixed point theorem. As applications, two examples are included to show the applicability of our results.

Keywords

• Initial value problem
• Caputo’s fractional derivative
• Sequential neutral functional differential equations
• Fractional integral
• Fixed point
• Existence