Hybrid Differential Inclusion Involving Two Multi-Valuedoperators with Nonlocal Multi-Valued Integral Condition

Ahmed Salem,Aeshah Al-Dosari

doi:10.3390/fractalfract6020109

Abstract

The present paper is devoted to the existence of solution for the Hybrid differential inclusions of the second type. Here, we present the inclusion problem with two multi-valued maps. In addition, it is considered with nonlocal integral boundary condition η(0)∈∫0σΔs,η(s)ds, where Δ is a multi-valued map. Relative compactness of the set ∫0σΔs,η(s)ds in L2(0,ε),R is used to justify the condensing condition for some created operators. Fixed point theorems connected with the weak compactness manner is utilized to explore the results throughout this paper.

Highlights

Among of a large amount contributions dedicated to study the existence and uniqueness of solution for Hybrid differential equations and inclusions with one multi-valued map, it is worth mentioning the works of Dhage [1,2], Dhage and Lakishmikantham [3]
The second is the generalization of infinite countable system of fractional differential equation into inclusion type
The authors in [7] were coming with a specific general formula of fractional differential equations and inclusions and they called this formula by equi-inclusion problem

Summary

Introduction

Among of a large amount contributions dedicated to study the existence and uniqueness of solution for Hybrid differential equations and inclusions with one multi-valued map, it is worth mentioning the works of Dhage [1,2], Dhage and Lakishmikantham [3]. That focused on fixed point theorems to Hybrid operators and their applications For such example, Ahmad et al [4] explore the solvability for first and second type of Hybrid equations and inclusions with one multi-valued map. It should be noted that Alzabut et al [8] worked great to investigate the novel solvability techniques on the generalized φ-Caputo fractional inclusion boundary problem. We consider the following Hybrid fractional differential inclusion associated with multi-valued maps Z and E

Objectives

Results

Conclusion