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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

Bashir Ahmad
  • Department of Mathematics Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia
  • Email:
/ Sotiris Ntouyas
  • Department of Mathematics, University of Ioannina, 451 10, Ioannina, Greece
  • Email:
Published Online: 2014-03-21 | DOI: https://doi.org/10.2478/s13540-014-0173-5

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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About the article

Published Online: 2014-03-21

Published in Print: 2014-06-01


Citation Information: Fractional Calculus and Applied Analysis, ISSN (Online) 1314-2224, DOI: https://doi.org/10.2478/s13540-014-0173-5.

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

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