Mathematical analysis of impulsive fractional differential inclusion of pantograph type

Abstract

In this article, we formulate fractional differential inclusion of pantograph type (IFDIP), incorporating impulsive behavior of the solution. The boundary conditions taken into account are nonlocal in nature. We will consider the convex problem and prove the Filippov–Wazewski‐type theorem. Moreover, existence of solution, uniqueness of a solution, and the topological properties of the solution's set will be examined for the problem under consideration. In the second part, the study will be confined to the second‐order impulsive fractional differential equation of pantograph type. For certain geometric characteristics of the solution's set, Aronszajn–Browder–Gupta‐type results will be explored for the newly introduced differential equation. Also, it will prove the existence of solution for the first‐order fractional differential equation of pantograph type having impulsive behavior of the solution.