Impulsive initial value problems for a class of implicit fractional differential equations

Abstract

In this article we consider, impulsive initial value problems for a class of implicit fractional differential equations involving the Caputo fractional derivative of order β in (1,2]. The solutions of this nonlinear equation are analyzed by establishing sufficient conditions for existence and uniqueness using Banach's contraction mapping principle and the Schaefer's fixed point theorem. In addition, using the Banach contraction principle, we establish uniqueness result. To demonstrate main results two examples are presented.