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Fractional Calculus and Applied Analysis

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A fully Hadamard type integral boundary value problem of a coupled system of fractional differential equations

1Department of Mathematics Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia

2Department of Mathematics, University of Ioannina, 451 10, Ioannina, Greece

© 2014 Diogenes Co., Sofia. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. (CC BY-NC-ND 3.0)

Citation Information: Fractional Calculus and Applied Analysis. Volume 17, Issue 2, Pages 348–360, ISSN (Online) 1314-2224, DOI: 10.2478/s13540-014-0173-5, March 2014

Publication History

Published Online:
2014-03-21

Abstract

This paper is concerned with the existence and uniqueness of solutions for a coupled system of Hadamard type fractional differential equations and integral boundary conditions. We emphasize that much work on fractional boundary value problems involves either Riemann-Liouville or Caputo type fractional differential equations. In the present work, we have considered a new problem which deals with a system of Hadamard differential equations and Hadamard type integral boundary conditions. The existence of solutions is derived from Leray-Schauder’s alternative, whereas the uniqueness of solution is established by Banach’s contraction principle. An illustrative example is also included.

MSC: Primary 34A08; Secondary 34A12, 34B15

Keywords: Hadamard fractional derivative; fractional differential systems; integral boundary conditions; fixed point theorems

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