Results on Hilfer Fractional Switched Dynamical System With Non-Instantaneous Impulses

Abstract

This paper concerns with the existence, uniqueness, Ulam's Hyer (UH) stability and total controllability results for the Hilfer fractional switched impulsive systems in finite-dimensional spaces. Mainly, this paper can be divided into three parts. In the first part, we examine the existence of a unique solution. In the second part, we establish the UH stability results, and in the third part, we study the total controllability results. The main outcomes are acquired by utilising the nonlinear analysis, fractional calculus, Mittag-Leffler function and Banach contraction principle. Finally, we have given two examples to validate the obtained analytical results.