Existence of Solutions of Impulsive Partial Hyperbolic Differential Inclusion of Fractional Order

Abstract

This paper is concerned with the existence of solutions of a class of Cauchy problems for hyperbolic partial fractional differential inclusions (HPFD) involving the Caputo fractional derivative with an impulse whose right hand side is convex and non-convex valued. Our results are achieved within the framework of the nonlinear alternative of Leray-Schauder type and contraction multivalued maps. A detailed example was provided to support the theorem.

Keywords

• differential inclusions
• impulse
• Caputo fractional derivative
• setvalued map