Existence of mild solution for nonlocal impulsive fractional semilinear differential inclusion in Banach space

Nawal Mohammed ,Kirtiwant P. Ghadle

doi:10.28919/jmcs/3815

Abstract

In this paper, we deal with the existence of PC-mild solutions of nonlocal impulsive differential inclusions in Banach space when the values of the orient field is convex (P). By using methods and results of semilinear differential inclusions, and techniques of fixed point theorems, we establish sufficient conditions that guarantee the existence of PC-mild solutions of (P). Our results develop and extend various results proved recently.

Highlights

Fractional differential equations and fractional differential inclusions have been an object of interest since two decades due to their wide applications in various fields, such as physics, biology, mechanics and engineering, medical field, industry and technology
We deal with the existence of PC-mild solutions of nonlocal impulsive differential inclusions in Banach space when the values of the orient field is convex (P)
By using methods and results of semilinear differential inclusions, and techniques of fixed point theorems, we establish sufficient conditions that guarantee the existence of PC-mild solutions of (P)

Summary

Introduction

Fractional differential equations and fractional differential inclusions have been an object of interest since two decades due to their wide applications in various fields, such as physics, biology, mechanics and engineering, medical field, industry and technology. We are concerned with the existence of mild solution for the following impulsive nonlocal Cauchy problem of fractional order α ∈ (0, 1) driven by a semilinear differential inclusion in a real separable Banach space E of the form. The main goal for many mathematicians has been to establish sufficient conditions regarding the existence of mild solution for differential equations or inclusions problems. Motivated by the above works, by using properties of multifunctions, some methods and results semilinear differential inclusions, and fixed point theorems, we develop the results shown in [16] as well as we extend the results in [23] to the case when (P) is taken with impulsive and nonlocal conditions. We used the properties of multifunctions, methods and results regarding semilinear differential inclusions, and fixed point techniques to obtain the results

Preliminaries

Main results

CONCLUSION