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Cauchy Problem for a Linear System of Ordinary Differential Equations of the Fractional Order

Author

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  • Murat Mamchuev

    (Institute of Applied Mathematics and Automation, Kabardin-Balkar Scientific Center of Russian Academy of Sciences, 89-A Shortanov Street, 360000 Nalchik, Russia)

Abstract

We investigate the initial problem for a linear system of ordinary differential equations with constant coefficients and with the Dzhrbashyan–Nersesyan fractional differentiation operator. The existence and uniqueness theorems of the solution of the boundary value problem under the study are proved. The solution is constructed explicitly in terms of the Mittag–Leffler function of the matrix argument. The Dzhrbashyan–Nersesyan operator is a generalization of the Riemann–Liouville, Caputo and Miller–Ross fractional differentiation operators. The obtained results as particular cases contain the results related to the study of initial problems for the systems of ordinary differential equations with Riemann–Liouville, Caputo and Miller–Ross derivatives and the investigated initial problem that generalizes them.

Suggested Citation

  • Murat Mamchuev, 2020. "Cauchy Problem for a Linear System of Ordinary Differential Equations of the Fractional Order," Mathematics, MDPI, vol. 8(9), pages 1-11, September.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1475-:d:407218
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    Cited by:

    1. Yekimov, Sergey, 2023. "The use of complex variable functions in economic and mathematical models, using the example of the international trade model of the Visegrad four countries for 2000-2015," MPRA Paper 117040, University Library of Munich, Germany.

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