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The Darboux problem for an implicit fractional-order differential equation

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Abstract

We obtain the sufficient conditions of the existence and uniqueness of a solution of the Darboux problem for an implicit fractional-order differential equation. A numerical method of solution of this problem is proposed.

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Authors and Affiliations

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

    Aleksandr Nikanorovich Vityuk

  2. Odessa State Economic University, 8, Preobrazhenskaya Str., Odessa, 65000, Ukraine

    Anastasiya Vital’evna Mykhailenko

Authors
  1. Aleksandr Nikanorovich Vityuk
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  2. Anastasiya Vital’evna Mykhailenko
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Correspondence to Aleksandr Nikanorovich Vityuk.

Additional information

Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 7, No. 4, pp. 439–452, October–November, 2010.

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Nikanorovich Vityuk, A., Vital’evna Mykhailenko, A. The Darboux problem for an implicit fractional-order differential equation. J Math Sci 175, 391–401 (2011). https://doi.org/10.1007/s10958-011-0353-3

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  • DOI: https://doi.org/10.1007/s10958-011-0353-3

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