Existence Results for Sequential Riemann–Liouville and Caputo Fractional Differential Inclusions with Generalized Fractional Integral Conditions

Mathematics

SotirisK. Ntouyas¹  Jessada Tariboon²  Bashir Ahmad³  Ahmed Alsaedi³ 

[1] Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece;Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand;Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia;

关键词: Riemann–Liouville fractional derivative;    Caputo fractional derivative;    inclusions;    endpoint theory;    generalized fractional integral;    Krasnosel’skiĭ’s multi-valued fixed point theorem;   

DOI  :  10.3390/math8061044

来源: DOAJ

【 摘 要 】

Under different criteria, we prove the existence of solutions for sequential fractional differential inclusions containing Riemann–Liouville and Caputo type derivatives and supplemented with generalized fractional integral boundary conditions. Our existence results rely on the endpoint theory, the Krasnosel’skiĭ’s fixed point theorem for multivalued maps and Wegrzyk’s fixed point theorem for generalized contractions. We demonstrate the application of the obtained results with the help of examples.

【 授权许可】

Unknown