Existence and Stability of Solutions for Bilinear Control System with Rieman-Leovel Initial Condition

Abstract

In this paper, we shall study the existence of a new class called fractional Caputo type of order sobolev type fractional order differential Equations motion in separable Banach spaces. The class of impulsive nonlinear fractional order bilinear control differential Equations with Riemann Leovel differential initial value studied and discussed also given the important results for the almost periodic mild solution to be sTable by using Menards function and granwal fractional inequality.

Keywords

• fractional Caputo differential, Riemann Leovel differential, Menards function, granwal fractional inequality.