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Random solutions to a system of fractional differential equations via the Hadamard fractional derivative

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Abstract

In this work, we use a new random fixed point theorem in vector metric spaces due to Sinacer et al. [M.L. Sinacer et al., Random Oper. Stoch. Equ. 24, 93 (2016)] to prove the existence of solutions and the compactness of solution sets of a random system of fractional differential equations via the Hadamard-type derivative. The existence, modification and stochastically continuity of an M2-solution are also proved.

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Authors and Affiliations

  1. Laboratory of Mathematics, University of Sidi Bel Abbés, P.O. Box 89, 22000, Sidi-Bel-Abbés, Algeria

    Mostefa Seghier & Abdelghani Ouahab

  2. Department of Mathematics, Baylor University, Waco, Texas, 76798-7328, USA

    Johnny Henderson

Authors
  1. Mostefa Seghier
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  2. Abdelghani Ouahab
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  3. Johnny Henderson
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Correspondence to Abdelghani Ouahab.

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Seghier, M., Ouahab, A. & Henderson, J. Random solutions to a system of fractional differential equations via the Hadamard fractional derivative. Eur. Phys. J. Spec. Top. 226, 3525–3549 (2017). https://doi.org/10.1140/epjst/e2018-00029-y

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