Hilfer fractional differential inclusions with Erdélyi–Kober fractional integral boundary condition

Advances in Difference Equations

Bahaaeldin Abdalla¹  Thabet Abdeljawad²  Abdelouaheb Ardjouni³  Adel Lachouri⁴  Mohammed S. Abdo⁵ 

[1] Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, Saudi Arabia;Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, Saudi Arabia;Department of Medical Research, China Medical University, 40402, Taichung, Taiwan;Department of Computer Science and Information Engineering, Asia University, Taichung, Taiwan;Department of Mathematics and Informatics, University of Souk Ahras, P.O. Box 1553, 41000, Souk Ahras, Algeria;Department of Mathematics, Annaba University, P.O. Box 12, 23000, Annaba, Algeria;Department of Mathematics, Hodeidah University, Al-Hodeidah, Yemen;

关键词: Fractional inclusion problem;    Hilfer and Erdélyi–Kober fractional operators;    Existence;    Fractional integral boundary conditions;    Convex;    Nonconvex;    Fixed point theorems;    34A08;    34A12;    34B15;   

DOI  :  10.1186/s13662-021-03397-7

来源: Springer

【 摘 要 】

In this article, we debate the existence of solutions for a nonlinear Hilfer fractional differential inclusion with nonlocal Erdélyi–Kober fractional integral boundary conditions (FIBC). Both cases of convex- and nonconvex-valued right-hand side are considered. Our obtained results are new in the framework of Hilfer fractional derivative and Erdélyi–Kober fractional integral with FIBC via the fixed point theorems (FPTs) for a set-valued analysis. Some pertinent examples demonstrating the effectiveness of the theoretical results are presented.

【 授权许可】

CC BY