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Discrete Approximation of Solutions of the Cauchy Problem for a Linear Homogeneous Differential-Operator Equation with a Caputo Fractional Derivative in a Banach Space

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Abstract

In this paper, we construct and examine the time-discretization scheme for the Cauchy problem for a linear homogeneous differential equation with the Caputo fractional derivative of order α ∈ (0, 1) in time and containing the sectorial operator in a Banach space in the spatial part. The convergence of the scheme is established and error estimates are obtained in terms of the step of discretization. Properties of the Mittag-Leffler function, hypergeometric functions, and the calculus of sectorial operators in Banach spaces are used. Results of numerical experiments that confirm theoretical conclusions are presented.

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Authors and Affiliations

  1. Mari State University, Yoshkar-Ola, Russia

    M. M. Kokurin

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  1. M. M. Kokurin
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Correspondence to M. M. Kokurin.

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 175, Proceedings of the XVII All-Russian Youth School-Conference “Lobachevsky Readings-2018,” November 23-28, 2018, Kazan. Part 1, 2020.

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Kokurin, M.M. Discrete Approximation of Solutions of the Cauchy Problem for a Linear Homogeneous Differential-Operator Equation with a Caputo Fractional Derivative in a Banach Space. J Math Sci 272, 826–852 (2023). https://doi.org/10.1007/s10958-023-06476-0

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