CAPUTO-TYPE FRACTIONAL SYSTEMS WITH VARIABLE ORDER DEPENDING ON THE IMPULSES AND CHANGING THE KERNEL

Abstract

In this paper, we introduce a new class of fractional impulsive systems of functions with respect to another function in which the order of the fractional derivative and the kernel function is associated with the impulses. We derive the solution representation, investigate the existence, and uniqueness of solutions of such a Caputo-type fractional impulsive system. Besides, the data dependence of the system is discussed. Our arguments are based on some classical fixed-point styles. Three various examples are provided to illustrate the validation of the main results. An open problem is presented in the conclusion section to bring the attention to a more general setting.