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Erschienen in:

13.03.2022 | Original Article

Optimal solution of a general class of nonlinear system of fractional partial differential equations using hybrid functions

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

Erschienen in: Engineering with Computers | Ausgabe 4/2023

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Abstract

This paper introduces a general class of nonlinear system of fractional partial differential equations with initial and boundary conditions. A hybrid method based on the transcendental Bernstein series and the generalized shifted Chebyshev polynomials is proposed for finding the optimal solution of the nonlinear system of fractional partial differential equations. The solution of the nonlinear system of fractional partial differential equations is expanded in terms of the transcendental Bernstein series and the generalized shifted Chebyshev polynomials, as basis functions with unknown free coefficients and control parameters. The corresponding operational matrices of fractional derivatives are then derived for the basis functions. These basis functions, with their operational matrices of fractional order derivatives and the Lagrange multipliers, transform the problem into a nonlinear system of algebraic equations. By means of Darbo’s fixed point theorem and Banach contraction principle, an existence result and a unique result for the solution of the nonlinear system of fractional partial differential equations are obtained, respectively. The convergence analysis is discussed and several illustrative experiments illustrate the efficiency and accuracy of the proposed method.

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Metadaten
Titel
Optimal solution of a general class of nonlinear system of fractional partial differential equations using hybrid functions
verfasst von
H. Hassani
J. A. Tenreiro Machado
E. Naraghirad
Z. Avazzadeh
Publikationsdatum
13.03.2022
Verlag
Springer London
Erschienen in
Engineering with Computers / Ausgabe 4/2023
Print ISSN: 0177-0667
Elektronische ISSN: 1435-5663
DOI
https://doi.org/10.1007/s00366-022-01627-4