Analyzing the convergence of a semi-numerical-analytical scheme for non-linear fractional PDEs
The purpose of this work is to develop a semi-analytical numerical scheme for solving fractional order non-linear partial differential equations (FOPDEs), particularly inhomogeneous FOPDEs, expressed in terms of the Caputo-Fabrizio fractional order derivative operator. To achieve this goal, we exami...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2023-09-01
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| Series: | Alexandria Engineering Journal |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016823005823 |
| _version_ | 1797736873330737152 |
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| author | Javed Iqbal Khurram Shabbir Amelia Bucur Azhar Ali Zafar |
| author_facet | Javed Iqbal Khurram Shabbir Amelia Bucur Azhar Ali Zafar |
| author_sort | Javed Iqbal |
| collection | DOAJ |
| description | The purpose of this work is to develop a semi-analytical numerical scheme for solving fractional order non-linear partial differential equations (FOPDEs), particularly inhomogeneous FOPDEs, expressed in terms of the Caputo-Fabrizio fractional order derivative operator. To achieve this goal, we examine several fractional versions of nonlinear model equations from the literature. We then present the proposed scheme, discussing its stability and convergence properties. We show that the proposed scheme is efficient and accurate, and we provide numerical examples to illustrate its performance. Our findings demonstrate that the scheme has significant potential for solving a wide range of complex FOPDEs. Overall, this work contributes to the advancement of numerical techniques for solving fractional order non-linear partial differential equations and lays a foundation for further research in this area. |
| first_indexed | 2024-03-12T13:20:23Z |
| format | Article |
| id | doaj.art-607594f031df43e98b9a52db4ad918ff |
| institution | Directory Open Access Journal |
| issn | 1110-0168 |
| language | English |
| last_indexed | 2024-03-12T13:20:23Z |
| publishDate | 2023-09-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj.art-607594f031df43e98b9a52db4ad918ff2023-08-26T04:42:50ZengElsevierAlexandria Engineering Journal1110-01682023-09-01782634Analyzing the convergence of a semi-numerical-analytical scheme for non-linear fractional PDEsJaved Iqbal0Khurram Shabbir1Amelia Bucur2Azhar Ali Zafar3Department of Mathematics, Government College University, Lahore, PakistanDepartment of Mathematics, Government College University, Lahore, Pakistan; Corresponding authors.Lucian Blaga University of Sibiu, Faculty of Sciences, Department of Mathematics and Informatics, I.Ratiu Street, no.5-7, 550012, Sibiu, Romania; Corresponding authors.Department of Mathematics, Government College University, Lahore, PakistanThe purpose of this work is to develop a semi-analytical numerical scheme for solving fractional order non-linear partial differential equations (FOPDEs), particularly inhomogeneous FOPDEs, expressed in terms of the Caputo-Fabrizio fractional order derivative operator. To achieve this goal, we examine several fractional versions of nonlinear model equations from the literature. We then present the proposed scheme, discussing its stability and convergence properties. We show that the proposed scheme is efficient and accurate, and we provide numerical examples to illustrate its performance. Our findings demonstrate that the scheme has significant potential for solving a wide range of complex FOPDEs. Overall, this work contributes to the advancement of numerical techniques for solving fractional order non-linear partial differential equations and lays a foundation for further research in this area.http://www.sciencedirect.com/science/article/pii/S1110016823005823Sequences and seriesCalculus of variationsVariational iteration methodLaplace transformNonlinear partial differential equationsFractional order derivative operators |
| spellingShingle | Javed Iqbal Khurram Shabbir Amelia Bucur Azhar Ali Zafar Analyzing the convergence of a semi-numerical-analytical scheme for non-linear fractional PDEs Alexandria Engineering Journal Sequences and series Calculus of variations Variational iteration method Laplace transform Nonlinear partial differential equations Fractional order derivative operators |
| title | Analyzing the convergence of a semi-numerical-analytical scheme for non-linear fractional PDEs |
| title_full | Analyzing the convergence of a semi-numerical-analytical scheme for non-linear fractional PDEs |
| title_fullStr | Analyzing the convergence of a semi-numerical-analytical scheme for non-linear fractional PDEs |
| title_full_unstemmed | Analyzing the convergence of a semi-numerical-analytical scheme for non-linear fractional PDEs |
| title_short | Analyzing the convergence of a semi-numerical-analytical scheme for non-linear fractional PDEs |
| title_sort | analyzing the convergence of a semi numerical analytical scheme for non linear fractional pdes |
| topic | Sequences and series Calculus of variations Variational iteration method Laplace transform Nonlinear partial differential equations Fractional order derivative operators |
| url | http://www.sciencedirect.com/science/article/pii/S1110016823005823 |
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