Solvability of a Coupled System of Fractional Differential Equations with Nonlocal and Integral Boundary Conditions

Issue title: Theory and Applications of Fractional Fourier Transform and its Variants

Guest editors: Yudong Zhang, Xiao-Jun Yang, Carlo Cattani, Zhengchao Dong, Ti-Fei Yuan and Liang-Xiu Han

Article type: Research Article

Authors: Ahmad, Bashir^* | Ntouyas, Sotiris K.^† | Alsaedi, Ahmed | Hobiny, Aatef

Affiliations: 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. bashirahmad_qau@yahoo.com, {aalsaedi, t.aatef}@hotmail.com, sntouyas@uoi.gr

Correspondence: [*] Address for correspondence: 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

Note: [†] Also affiliated at: Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece

Abstract: This paper is concerned with the existence and uniqueness of solutions for a coupled system of fractional differential equations with nonlocal and integral boundary conditions. The existence and uniqueness of solutions is established by Banach’s contraction principle, while the existence of solutions is derived by using Leray-Schauder’s alternative. The results are explained with the aid of examples. The case of nonlocal strip conditions is also discussed.

Keywords: Fractional differential equations, coupled system, nonlocal conditions, integral boundary conditions, fixed point theorems

DOI: 10.3233/FI-2017-1481

Journal: Fundamenta Informaticae, vol. 151, no. 1-4, pp. 91-108, 2017