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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| Veröffentlicht in: | Advances in difference equations Jg. 2020; H. 1; S. 1 - 23 |
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| Abstract | 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. |
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| AbstractList | 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. Abstract 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. |
| ArticleNumber | 494 |
| Author | Osman, M. S. Ali, Khalid K. Mohamed, Emad M. H. Samet, Bessem Abd El Salam, Mohamed A. Kumar, Sunil |
| Author_xml | – sequence: 1 givenname: Khalid K. surname: Ali fullname: Ali, Khalid K. organization: Department of Mathematics, Faculty of Science, Al Azhar University – sequence: 2 givenname: Mohamed A. surname: Abd El Salam fullname: Abd El Salam, Mohamed A. organization: Department of Mathematics, Faculty of Science, Al Azhar University – sequence: 3 givenname: Emad M. H. surname: Mohamed fullname: Mohamed, Emad M. H. organization: Department of Mathematics, Faculty of Science, Al Azhar University – sequence: 4 givenname: Bessem surname: Samet fullname: Samet, Bessem organization: Department of Mathematics, College of Science, King Saud University – sequence: 5 givenname: Sunil orcidid: 0000-0001-5420-8147 surname: Kumar fullname: Kumar, Sunil email: skumar.math@nitjsr.ac.in organization: Department of Mathematics, National Institute of Technology – sequence: 6 givenname: M. S. surname: Osman fullname: Osman, M. S. email: mofatzi@sci.cu.edu.eg organization: Department of Mathematics, Faculty of Science, Cairo University |
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| SubjectTerms | 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 |
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| Title | Numerical solution for generalized nonlinear fractional integro-differential equations with linear functional arguments using Chebyshev series |
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