Existence of solution for impulsive fractional qr-difference equation of implicit form with nonlocal boundary condition

Abstract

This study examines the conditions needed for the existence of solutions to an impulsive fractional qr-difference equation with the implicit form. The fractional derivative we analyze in the problem is of the Caputo type, which involves a q-shifting operator of the form aϕq(u) = qu+ (1−q)a. Here, nonlocal conditions are the boundary conditions we take into account. Regarding the existence of solutions for the given problem, the result is obtained by means of Krasnoselskii’s fixed point theorem. In addition, circumstances required for the Ulam-Hyers and Generalized Ulam-Hyers stability of the impulsive problem are explored. Finally, we provide an example to demonstrate our findings.