On the existence of solutions to fractional differential equations involving Caputo q-derivative in Banach spaces
Isra Al-Shbeil,
Houari Bouzid,
Benali Abdelkader,
Alina Alp Lupas,
Mohammad Esmael Samei,
Reem K. Alhefthi
Affiliations
Isra Al-Shbeil
Department of Mathematics, Faculty of Sciences, The University of Jordan, 11942 Amman, Jordan; Corresponding author.
Houari Bouzid
Department of Mathematics, Faculty of Exact Science and Informatics, Hassiba Benbouali University of Chlef, Ouled Fares, Chlef 02000, Laboratory of Mathematics and Applications (LMA), Algeria
Benali Abdelkader
Department of Mathematics, Faculty of Exact Science and Informatics, Hassiba Benbouali University of Chlef, Ouled Fares, Chlef 02000, Laboratory of Mathematics and Applications (LMA), Algeria
Alina Alp Lupas
Department of Mathematics and Computer Sciences, University of Oradea, 10087 Oradea, Romania
Mohammad Esmael Samei
Department of Mathematics, Faculty of Science, Bu-Ali Sina University, Hamedan, Iran
Reem K. Alhefthi
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
The generalization of BVPs always covers a wide range of equations. Our choice in this research is the generalization of Caputo-type fractional discrete differential equations that include two or more fractional q-integrals. We analyze the existence and uniqueness of solutions to the multi-point nonlinear BVPs base on fixed point theory, including fixed point theorem of Banach, Leray-nonlinear Schauder's alternative, and Leray-degree Schauder's theory. Finally, several examples are presented to demonstrate accuracy of our results.
