BVP for Hadamard Sequential Fractional Hybrid Differential Inclusions

Ning Li,Yiru Chen,Haibo Gu,Mohamed A Taoudi

doi:10.1155/2022/4042483

Ning Li, Yiru Chen + Show 2 more

Open Access

https://doi.org/10.1155/2022/4042483

Copy DOI

Abstract

The study is concerned with the Hadamard sequential fractional hybrid differential inclusions with two-point hybrid integral boundary conditions. With the help of the Dhage fixed-point theorem for the product of two operators and the Covitz-Nadler fixed-point theorem in the case of fractional inclusions, we obtain the existence results of solutions for Hadamard sequential fractional hybrid differential inclusions. Finally, two examples are presented to illustrate the main results.

Highlights

Nowadays, with the increasing demand of researchers for the study of natural phenomena, the use of fractional differential operators and fractional differential equations become an effective means to achieve this goal
We need to study more natural phenomena to gain more abilities for modeling. erefore, fractional calculus came into being, and today, their importance has become more and more apparent to researchers
We have developed the existence theory for a class of Hadamard sequential fractional hybrid differential inclusions equipped with two-point hybrid Hadamard integral boundary value conditions. e nonlinearities in the given problems implicitly depend on the unknown function together with its Hadamard fractional integral of order p ∈ (0, 1)

Summary

Introduction

With the increasing demand of researchers for the study of natural phenomena, the use of fractional differential operators and fractional differential equations become an effective means to achieve this goal. In [47], by using a hybrid fixed-point theorem of Schaefer type for a sum of three operators due to Dhage, the authors investigated the existence of solutions for the nonlocal fractional BVP of hybrid inclusion problem given by. E Hadamard sequential fractional hybrid differential inclusion BVP (7) is modeled with respect to the generalized operators with kernels, including logarithmic functions. We express that such a Hadamard sequential fractional hybrid differential inclusion BVP is new and enriches the literature on boundary value problems for nonlinear Hadamard fractional differential inclusions In this way, with the help of Dhage fixed-point theorem and Covitz-Nadler fixed-point theorem in the case of multivalued mapping, we try to find the existence criteria of solutions for the proposed problem (7).

Preliminaries

Main Results

Conclusion