INVESTIGATION OF INTEGRAL BOUNDARY VALUE PROBLEM WITH IMPULSIVE BEHAVIOR INVOLVING NON-SINGULAR DERIVATIVE
Kamal Shah, Thabet Abdeljawad, Arshad Ali, Manar A. Alqudah
Abstract
This paper is devoted to investigating a class of impulsive fractional order differential equations (FODEs) with integral boundary condition. For the proposed paper, we use non-singular type derivative of fractional order which has been introduced by Atangana, Baleanu and Caputo (ABC). The aforesaid type problems have numerous applications in fluid mechanics and hydrodynamics to model various problems of flow phenomenons. We establish some sufficient conditions for the existence and uniqueness of solution to the proposed problem by using classical fixed point results due to Banach and Krasnoselskii. Further, on using tools of the nonlinear analysis, sufficient conditions are developed for Hyers–Ulam (HU) type stability results. A pertinent example is given to justify our results.