Coupled systems of Riemann-Liouville fractional differential equations with Hadamard fractional integral boundary conditions

Volume 9, Issue 1, pp 295--308 http://dx.doi.org/10.22436/jnsa.009.01.28

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Authors

Jessada Tariboon - Nonlinear Dynamic Analysis Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok, 10800, Thailand. Sotiris K. Ntouyas - Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece. - 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. Weerawat Sudsutad - Nonlinear Dynamic Analysis Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok, 10800, Thailand.

Abstract

In this paper we study existence and uniqueness of solutions for coupled systems consisting from fractional differential equations of Riemann-Liouville type subject to coupled and uncoupled Hadamard fractional 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. Examples illustrating our results are also presented.

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Keywords

• Riemann-Liouville fractional derivative
• Hadamard fractional integral
• coupled system
• existence
• uniqueness
• fixed point theorems.

MSC

•  34A08
•  34B15

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