Using Fractional Bernoulli Wavelets for Solving Fractional Diffusion Wave Equations with Initial and Boundary Conditions
In this paper, fractional-order Bernoulli wavelets based on the Bernoulli polynomials are constructed and applied to evaluate the numerical solution of the general form of Caputo fractional order diffusion wave equations. The operational matrices of ordinary and fractional derivatives for Bernoulli...
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| مؤلفون آخرون: | , , |
| التنسيق: | article |
| منشور في: |
2021
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| الموضوعات: | |
| الوصول للمادة أونلاين: | http://hdl.handle.net/11073/23902 |
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| _version_ | 1864513440765181952 |
|---|---|
| author | Sahlan, Monireh Nosrati |
| author2 | Afshari, Hojjat Alzabut, Jehad Alobaidi, Ghada |
| author2_role | author author author |
| author_facet | Sahlan, Monireh Nosrati Afshari, Hojjat Alzabut, Jehad Alobaidi, Ghada |
| author_role | author |
| dc.creator.none.fl_str_mv | Sahlan, Monireh Nosrati Afshari, Hojjat Alzabut, Jehad Alobaidi, Ghada |
| dc.date.none.fl_str_mv | 2021 2022-06-02T09:55:17Z 2022-06-02T09:55:17Z |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | Sahlan, M.N.; Afshari, H.; Alzabut, J.; Alobaidi, G. Using Fractional Bernoulli Wavelets for Solving Fractional Diffusion Wave Equations with Initial and Boundary Conditions. Fractal Fract. 2021, 5, 212. https://doi.org/10.3390/ fractalfract5040212. [Comment: This article belongs to the Section General Mathematics, Analysis] 2504-3110 http://hdl.handle.net/11073/23902 10.3390/ fractalfract5040212 |
| dc.language.none.fl_str_mv | en_US |
| dc.publisher.none.fl_str_mv | MDPI |
| dc.relation.none.fl_str_mv | https://doi.org/10.3390/fractalfract5040212 |
| dc.subject.none.fl_str_mv | Fractional bernoulli wavelets Operational matrix Diffusion wave equation Klein–Gordon equation |
| dc.title.none.fl_str_mv | Using Fractional Bernoulli Wavelets for Solving Fractional Diffusion Wave Equations with Initial and Boundary Conditions |
| dc.type.none.fl_str_mv | Peer-Reviewed Published version info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/article |
| description | In this paper, fractional-order Bernoulli wavelets based on the Bernoulli polynomials are constructed and applied to evaluate the numerical solution of the general form of Caputo fractional order diffusion wave equations. The operational matrices of ordinary and fractional derivatives for Bernoulli wavelets are set via fractional Riemann–Liouville integral operator. Then, these wavelets and their operational matrices are utilized to reduce the nonlinear fractional problem to a set of algebraic equations. For solving the obtained system of equations, Galerkin and collocation spectral methods are employed. To demonstrate the validity and applicability of the presented method, we offer five significant examples, including generalized Cattaneo diffusion wave and Klein–Gordon equations. The implementation of algorithms exposes high accuracy of the presented numerical method. The advantage of having compact support and orthogonality of these family of wavelets trigger having sparse operational matrices, which reduces the computational time and CPU requirements. |
| format | article |
| id | aus_d8627da5b801d398e60133f893e65ace |
| identifier_str_mv | Sahlan, M.N.; Afshari, H.; Alzabut, J.; Alobaidi, G. Using Fractional Bernoulli Wavelets for Solving Fractional Diffusion Wave Equations with Initial and Boundary Conditions. Fractal Fract. 2021, 5, 212. https://doi.org/10.3390/ fractalfract5040212. [Comment: This article belongs to the Section General Mathematics, Analysis] 2504-3110 10.3390/ fractalfract5040212 |
| language_invalid_str_mv | en_US |
| network_acronym_str | aus |
| network_name_str | aus |
| oai_identifier_str | oai:repository.aus.edu:11073/23902 |
| publishDate | 2021 |
| publisher.none.fl_str_mv | MDPI |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| spelling | Using Fractional Bernoulli Wavelets for Solving Fractional Diffusion Wave Equations with Initial and Boundary ConditionsSahlan, Monireh NosratiAfshari, HojjatAlzabut, JehadAlobaidi, GhadaFractional bernoulli waveletsOperational matrixDiffusion wave equationKlein–Gordon equationIn this paper, fractional-order Bernoulli wavelets based on the Bernoulli polynomials are constructed and applied to evaluate the numerical solution of the general form of Caputo fractional order diffusion wave equations. The operational matrices of ordinary and fractional derivatives for Bernoulli wavelets are set via fractional Riemann–Liouville integral operator. Then, these wavelets and their operational matrices are utilized to reduce the nonlinear fractional problem to a set of algebraic equations. For solving the obtained system of equations, Galerkin and collocation spectral methods are employed. To demonstrate the validity and applicability of the presented method, we offer five significant examples, including generalized Cattaneo diffusion wave and Klein–Gordon equations. The implementation of algorithms exposes high accuracy of the presented numerical method. The advantage of having compact support and orthogonality of these family of wavelets trigger having sparse operational matrices, which reduces the computational time and CPU requirements.MDPI2022-06-02T09:55:17Z2022-06-02T09:55:17Z2021Peer-ReviewedPublished versioninfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfSahlan, M.N.; Afshari, H.; Alzabut, J.; Alobaidi, G. Using Fractional Bernoulli Wavelets for Solving Fractional Diffusion Wave Equations with Initial and Boundary Conditions. Fractal Fract. 2021, 5, 212. https://doi.org/10.3390/ fractalfract5040212. [Comment: This article belongs to the Section General Mathematics, Analysis]2504-3110http://hdl.handle.net/11073/2390210.3390/ fractalfract5040212en_UShttps://doi.org/10.3390/fractalfract5040212oai:repository.aus.edu:11073/239022024-08-22T12:01:46Z |
| spellingShingle | Using Fractional Bernoulli Wavelets for Solving Fractional Diffusion Wave Equations with Initial and Boundary Conditions Sahlan, Monireh Nosrati Fractional bernoulli wavelets Operational matrix Diffusion wave equation Klein–Gordon equation |
| status_str | publishedVersion |
| title | Using Fractional Bernoulli Wavelets for Solving Fractional Diffusion Wave Equations with Initial and Boundary Conditions |
| title_full | Using Fractional Bernoulli Wavelets for Solving Fractional Diffusion Wave Equations with Initial and Boundary Conditions |
| title_fullStr | Using Fractional Bernoulli Wavelets for Solving Fractional Diffusion Wave Equations with Initial and Boundary Conditions |
| title_full_unstemmed | Using Fractional Bernoulli Wavelets for Solving Fractional Diffusion Wave Equations with Initial and Boundary Conditions |
| title_short | Using Fractional Bernoulli Wavelets for Solving Fractional Diffusion Wave Equations with Initial and Boundary Conditions |
| title_sort | Using Fractional Bernoulli Wavelets for Solving Fractional Diffusion Wave Equations with Initial and Boundary Conditions |
| topic | Fractional bernoulli wavelets Operational matrix Diffusion wave equation Klein–Gordon equation |
| url | http://hdl.handle.net/11073/23902 |