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Nonlinear Functional Boundary Value Problems for Conformable Fractional Dynamic Equations on Time Scales

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Abstract

In this paper, we establish the existence of solutions for the conformable fractional dynamic equations on time scales, with nonlinear functional boundary value conditions. We first obtain the exact expression of the fractional Green’s function related to the linear conformable fractional dynamic problem and then we study the nonlinear functional boundary problems, by means of the upper and lower solutions method together with Schauder’s fixed-point theorem.

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Authors and Affiliations

  1. Ibn Khaldoun, Tiaret University, Zaâroura, P.O. Box 78, 14000, Tiaret, Algeria

    Bouharket Bendouma

  2. University of Sidi Bel Abbès, P.O. Box 89, 22000, Sidi Bel Abbès, Algeria

    Bouharket Bendouma

  3. Laboratory of Mathematics, Ain Témouchent University, P.O. Box 89, 46000, Ain Témouchent, Algeria

    Ahmed Hammoudi

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  1. Bouharket Bendouma
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  2. Ahmed Hammoudi
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Correspondence to Bouharket Bendouma.

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Bendouma, B., Hammoudi, A. Nonlinear Functional Boundary Value Problems for Conformable Fractional Dynamic Equations on Time Scales. Mediterr. J. Math. 16, 25 (2019). https://doi.org/10.1007/s00009-019-1302-5

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  • DOI: https://doi.org/10.1007/s00009-019-1302-5

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