Investigation of nonlinear Riemann-Liouville fractional differential equations with fractional nonlocal multi-point and integral boundary conditions

Bashir Ahmad; Hafed   Saeed; Ahmed Alsaedi; Sotiris  Ntouyas

doi:10.5269/bspm.75987

Investigation of nonlinear Riemann-Liouville fractional differential equations with fractional nonlocal multi-point and integral boundary conditions

Investigation of nonlinear Riemann-Liouville fractional differential equations

Bashir Ahmad 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
Hafed Saeed King Abdulaziz University https://orcid.org/0009-0007-8306-3056
Ahmed Alsaedi King Abdulaziz University https://orcid.org/0000-0003-3452-8922
Sotiris Ntouyas University of Ioannina https://orcid.org/0000-0002-7695-2118

DOI: https://doi.org/10.5269/bspm.75987

Abstract

We investigate the existence of solutions for a Riemann–Liouville fractional differential equation of order $\alpha \in (2, 3]$ equipped with fractional anti-periodic type nonlocal multi-point and Riemann–Liouville integral boundary conditions in a weighted space. The existence and uniqueness results for the given problem are respectively proved by applying the Leray-Schauder's alternative and the Banach's contraction mapping principle. The Ulam–Hyers stability for the given problem is also studied. Examples illustrating the main results are offered.