On Existence of Multiplicity of Weak Solutions for a New Class of Nonlinear Fractional Boundary Value Systems via Variational Approach-Reference-Cited by-同舟云学术

On Existence of Multiplicity of Weak Solutions for a New Class of Nonlinear Fractional Boundary Value Systems via Variational Approach

Published:2021-03-13 Issue: Volume:2021 Page:1-10
ISSN:1687-9139
Container-title:Advances in Mathematical Physics
language:en
Short-container-title:Advances in Mathematical Physics

Author:

Kamache Fares¹,Boulaaras Salah Mahmoud²³^ORCID,Guefaifia Rafik¹,Chung Nguyen Thanh⁴,Cherif Bahri Belkacem²⁵^ORCID,Abdalla Mohamed⁶⁷

Affiliation:

1. Laboratory of Mathematics, Informatics and Systems, Larbi Tebessi University, 12000 Tebessa, Algeria

2. Department of Mathematics, College of Sciences and Arts, ArRass, Qassim University, Saudi Arabia

3. Laboratory of Fundamental and Applied Mathematics of Oran (LMFAO), University of Oran 1, Oran, 31000 Oran, Algeria

4. Department of Mathematics, Quang Binh University, 312 Ly Thuong Kiet, Dong Hoi, Quang Binh, Vietnam

5. Preparatory Institute for Engineering Studies, Sfax, Tunisia

6. Mathematics Department, College of Science, King Khalid University, Abha 61413, Saudi Arabia

7. Mathematics Department, Faculty of Science, South Valley University, Qena 83523, Egypt

Abstract

This paper deals with the existence of solutions for a new class of nonlinear fractional boundary value systems involving the left and right Riemann-Liouville fractional derivatives. More precisely, we establish the existence of at least three weak solutions for the problem using variational methods combined with the critical point theorem due to Bonano and Marano. In addition, some examples in