Existence of Solution to Fractional Order Impulsive Partial Hyperbolic Differential Equations with Infinite Delay

Abstract

In this paper, we investigate the existence of solutions to a class of initial value problem for fractional order impulsive partial hyperbolic differential equations (for short FOIPHDEs) with infinite delay. Here we use Mixed Riemann-Liouville fractional derivative to construct the considered FOIPHDEs. The analysis of this paper is based on Burton-Krik fixed point theorem. A new existence result for FOIPHDEs with infinite delay has been obtained. To support the analytic proof, we give an illustrative example.