Random Solutions for Generalized Caputo Periodic and Non-Local Boundary Value Problems
Bashir Ahmad,
Mokhtar Boumaaza,
Abdelkrim Salim,
Mouffak Benchohra
Affiliations
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
Mokhtar Boumaaza
Faculty of Sciences and Technology, University of Ghardaia, P.O. Box 455, Ghardaia 47000, Algeria
Abdelkrim Salim
Faculty of Technology, Hassiba Benbouali University of Chlef, P.O. Box 151, Chlef 02000, Algeria
Mouffak Benchohra
Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbes, P.O. Box 89, Sidi Bel-Abbes 22000, Algeria
In this article, we present some results on the existence and uniqueness of random solutions to a non-linear implicit fractional differential equation involving the generalized Caputo fractional derivative operator and supplemented with non-local and periodic boundary conditions. We make use of the fixed point theorems due to Banach and Krasnoselskii to derive the desired results. Examples illustrating the obtained results are also presented.
