Numerical solution for generalized nonlinear fractional integro-differential equations with linear functional arguments using Chebyshev series

In the present work, a numerical technique for solving a general form of nonlinear fractional order integro-differential equations (GNFIDEs) with linear functional arguments using Chebyshev series is presented. The recommended equation with its linear functional argument produces a general form of d...

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Vydáno v:Advances in difference equations Ročník 2020; číslo 1; s. 1 - 23
Hlavní autoři: Ali, Khalid K., Abd El Salam, Mohamed A., Mohamed, Emad M. H., Samet, Bessem, Kumar, Sunil, Osman, M. S.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Cham Springer International Publishing 15.09.2020
Springer Nature B.V
SpringerOpen
Témata:
Analysis
Applications
Caputo fractional derivatives
Chebyshev approximation
Chebyshev collocation method
Collocation methods
Derivatives
Difference and Functional Equations
Differential equations
Functional Analysis
Functional argument
Mathematics
Mathematics and Statistics
Methods
Nonlinear equations
Nonlinear fractional integro-differential equations
Nonlinear systems
Ordinary Differential Equations
Partial Differential Equations
Topics in Special Functions and q-Special Functions: Theory
Functional argument
Nonlinear fractional integro-differential equations
Chebyshev collocation method
Caputo fractional derivatives
ISSN:1687-1847, 1687-1839, 1687-1847
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Popis
Shrnutí:In the present work, a numerical technique for solving a general form of nonlinear fractional order integro-differential equations (GNFIDEs) with linear functional arguments using Chebyshev series is presented. The recommended equation with its linear functional argument produces a general form of delay, proportional delay, and advanced non-linear arbitrary order Fredholm–Volterra integro-differential equations. Spectral collocation method is extended to study this problem as a matrix discretization scheme, where the fractional derivatives are characterized in the Caputo sense. The collocation method transforms the given equation and conditions to an algebraic nonlinear system of equations with unknown Chebyshev coefficients. Additionally, we present a general form of the operational matrix for derivatives. The introduced operational matrix of derivatives includes arbitrary order derivatives and the operational matrix of ordinary derivative as a special case. To the best of authors’ knowledge, there is no other work discussing this point. Numerical test examples are given, and the achieved results show that the recommended method is very effective and convenient.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-020-02951-z