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Fractional Differential Equations with Nonlocal Integral and Integer–Fractional-Order Neumann Type Boundary Conditions

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Abstract

We introduce a new concept of the coupling of nonlocal integral and integer–fractional-order Neumann type boundary conditions, and discuss the existence and uniqueness of solutions for a coupled system of fractional differential equations supplemented with these conditions. The existence of solutions is derived from Leray–Schauder’s alternative and Schauder’s fixed point theorem, while the uniqueness of solutions is established by means of Banach’s contraction mapping principle. The results obtained in this paper are well illustrated with the aid of examples.

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Authors and Affiliations

  1. Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group Faculty of Science, Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia

    Bashir Ahmad & Sotiris K. Ntouyas

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

    Sotiris K. Ntouyas

  3. Faculty of Applied Science, Department of Mathematics Nonlinear Dynamic Analysis Research Center, King Mongkut’s University of Technology North Bangkok, Bangkok, 10800, Thailand

    Jessada Tariboon

Authors
  1. Bashir Ahmad
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  2. Sotiris K. Ntouyas
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  3. Jessada Tariboon
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Correspondence to Bashir Ahmad.

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Ahmad, B., Ntouyas, S.K. & Tariboon, J. Fractional Differential Equations with Nonlocal Integral and Integer–Fractional-Order Neumann Type Boundary Conditions. Mediterr. J. Math. 13, 2365–2381 (2016). https://doi.org/10.1007/s00009-015-0629-9

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  • DOI: https://doi.org/10.1007/s00009-015-0629-9

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