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On one class of differential equations of fractional order

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Nonlinear Oscillations

We consider the Darboux problem for a differential equation of fractional order that contains a regularized mixed derivative. Sufficient conditions for the existence and uniqueness of a solution of this problem are obtained in the class of continuous functions. We also propose a method for finding an approximate solution of this problem and prove the convergence of this method.

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Authors and Affiliations

  1. Institute of Mathematics, Economics, and Mechanics, Odessa National University, Odessa, Ukraine

    A. N. Vityuk & A. V. Mikhailenko

Authors
  1. A. N. Vityuk
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  2. A. V. Mikhailenko
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Correspondence to A. N. Vityuk.

Additional information

Translated from Neliniini Kolyvannya, Vol. 11, No. 3, pp. 293–304, July–September, 2008.

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Vityuk, A.N., Mikhailenko, A.V. On one class of differential equations of fractional order. Nonlinear Oscill 11, 307–319 (2008). https://doi.org/10.1007/s11072-009-0032-1

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  • DOI: https://doi.org/10.1007/s11072-009-0032-1

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