An Approximate Solution to a Class of Impulsive Fractional Differential Equations in a Reflexive Banach Space

Abstract

In this manuscript, we considered a class of impulsive differential equations of order $$1<\alpha \le 2$$ in a reflexive Banach space X. By using the theory of semigroup of bounded linear operators and the theory of strongly continuous cosine families, we proved the existence and convergence of approximate solutions of an associated fractional integral equation to the considered problem. Abstract results are illustrated by an example in the last section.