A numerical computational technique for solving controllability of impulsive Hilfer fractional integro-differential equation with order ϑ∈(1,2)

Abstract

The primary focus of this paper is the concept of controllability criteria for the impulsive Hilfer fractional integro-differential equation (IHFrIDE) of order 0≤ϖ≤1 and 1<ϑ<2 in Hilbert space. We use the iterative process and the strongly cosine family to obtain a given system outcome. We use the degree method to demonstrate the existence of a solution for a given dynamical system. We obtained uniqueness results from Gronwall’s inequality and also addressed the controllability criteria for our given problem. The outputs of numerical computations demonstrate the efficiency of our present method.

Keywords

• Hilfer fractional derivative
• Strongly cosine family
• Degree theory
• Gronwall’s inequality