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

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...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2023-06, Vol.272 (6), p.826-852
Main Author: Kokurin, M. M.
Format: Article
Language:English
Subjects:
Banach spaces
Cauchy problems
Derivatives
Differential equations
Discretization
Fractional calculus
Hypergeometric functions
Mathematics
Mathematics and Statistics
Operators (mathematics)
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Summary: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.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-023-06476-0