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Engineering with Computers
Erschienen in: Engineering with Computers 3/2020

27.03.2019 | Original Article

Numerical approach for solving variable-order space–time fractional telegraph equation using transcendental Bernstein series

verfasst von: H. Hassani, Z. Avazzadeh, J. A. Tenreiro Machado

Erschienen in: Engineering with Computers | Ausgabe 3/2020

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Abstract

This paper presents the transcendental Bernstein series (TBS) as a generalization of the classical Bernstein polynomials for solving the variable-order space–time fractional telegraph equation (V-STFTE). An approximation method using optimization techniques and the TBS is introduced. The solution of the problem under consideration is expanded in terms of TBS with unknown free coefficients and control parameters. The new corresponding operational matrices of variable-order fractional derivatives, in the Caputo type, are derived. The proposed approach reduces the V-STFTE to a system of algebraic equations and, subsequently, to find the free coefficients and control parameters using the Lagrange multipliers technique. The convergence analysis of the method is guranteed by means of a new theorem concerning the TBS. The experimental results confirm the high accuracy and computational efficiency of the TBS method.
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Metadaten
Titel
Numerical approach for solving variable-order space–time fractional telegraph equation using transcendental Bernstein series
verfasst von
H. Hassani
Z. Avazzadeh
J. A. Tenreiro Machado
Publikationsdatum
27.03.2019
Verlag
Springer London
Erschienen in
Engineering with Computers / Ausgabe 3/2020
Print ISSN: 0177-0667
Elektronische ISSN: 1435-5663
DOI
https://doi.org/10.1007/s00366-019-00736-x

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