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On fractional order derivatives and Darboux problem for implicit differential equations

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Abstract

In this paper we prove some relations between the Riemann-Liouville and the Caputo fractional order derivatives, and we investigate the existence and uniqueness of solutions for the initial value problems (IVP for short), for a class of functional hyperbolic differential equations by using some fixed point theorems.

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Authors and Affiliations

  1. Laboratoire de Mathématiques, Université de Saïda, B.P. 138, 20000, Saïda, Algérie

    Saïd Abbas

  2. Laboratoire de Mathématiques, Université de Sidi Bel-Abbès, B.P. 89, 22000, Sidi Bel-Abbès, Algérie

    Mouffak Benchohra

  3. I. I. Mechnikov Odessa National University 2, Dvoryanskaya Str., Odessa, 65026, Ukraine

    Aleksandr N. Vityuk

Authors
  1. Saïd Abbas
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  2. Mouffak Benchohra
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  3. Aleksandr N. Vityuk
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Abbas, S., Benchohra, M. & Vityuk, A.N. On fractional order derivatives and Darboux problem for implicit differential equations. fcaa 15, 168–182 (2012). https://doi.org/10.2478/s13540-012-0012-5

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