Shifted Jacobi polynomials for nonlinear singular variable-order time fractional Emden–Fowler equation generated by derivative with non-singular kernel
Abstract In this work, a nonlinear singular variable-order fractional Emden–Fowler equation involved with derivative with non-singular kernel (in the Atangana–Baleanu–Caputo type) is introduced and a computational method is proposed for its numerical solution. The desired method is established upon...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-03-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13662-021-03349-1 |
| _version_ | 1818415559983759360 |
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| author | M. H. Heydari Z. Avazzadeh A. Atangana |
| author_facet | M. H. Heydari Z. Avazzadeh A. Atangana |
| author_sort | M. H. Heydari |
| collection | DOAJ |
| description | Abstract In this work, a nonlinear singular variable-order fractional Emden–Fowler equation involved with derivative with non-singular kernel (in the Atangana–Baleanu–Caputo type) is introduced and a computational method is proposed for its numerical solution. The desired method is established upon the shifted Jacobi polynomials and their operational matrix of variable-order fractional differentiation (which is extracted in the present study) together with the spectral collocation method. The presented method transforms obtaining the solution of the main problem into obtaining the solution of an algebraic system of equations. Several numerical examples are examined to show the validity and the high accuracy of the established method. |
| first_indexed | 2024-12-14T11:36:56Z |
| format | Article |
| id | doaj.art-3fef7794998b4173b390b8ff8f0df71a |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-14T11:36:56Z |
| publishDate | 2021-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-3fef7794998b4173b390b8ff8f0df71a2022-12-21T23:02:59ZengSpringerOpenAdvances in Difference Equations1687-18472021-03-012021111510.1186/s13662-021-03349-1Shifted Jacobi polynomials for nonlinear singular variable-order time fractional Emden–Fowler equation generated by derivative with non-singular kernelM. H. Heydari0Z. Avazzadeh1A. Atangana2Department of Mathematics, Shiraz University of TechnologyDepartment of Applied Mathematics, Xi’an Jiaotong-Liverpool UniversityFaculty of Natural and Agricultural Sciences, University of the Free StateAbstract In this work, a nonlinear singular variable-order fractional Emden–Fowler equation involved with derivative with non-singular kernel (in the Atangana–Baleanu–Caputo type) is introduced and a computational method is proposed for its numerical solution. The desired method is established upon the shifted Jacobi polynomials and their operational matrix of variable-order fractional differentiation (which is extracted in the present study) together with the spectral collocation method. The presented method transforms obtaining the solution of the main problem into obtaining the solution of an algebraic system of equations. Several numerical examples are examined to show the validity and the high accuracy of the established method.https://doi.org/10.1186/s13662-021-03349-1Shifted Jacobi polynomials (SJPs)Operational matricesVariable-order (VO) time fractional derivativeSingular VO time fractional Emden–Fowler equation |
| spellingShingle | M. H. Heydari Z. Avazzadeh A. Atangana Shifted Jacobi polynomials for nonlinear singular variable-order time fractional Emden–Fowler equation generated by derivative with non-singular kernel Advances in Difference Equations Shifted Jacobi polynomials (SJPs) Operational matrices Variable-order (VO) time fractional derivative Singular VO time fractional Emden–Fowler equation |
| title | Shifted Jacobi polynomials for nonlinear singular variable-order time fractional Emden–Fowler equation generated by derivative with non-singular kernel |
| title_full | Shifted Jacobi polynomials for nonlinear singular variable-order time fractional Emden–Fowler equation generated by derivative with non-singular kernel |
| title_fullStr | Shifted Jacobi polynomials for nonlinear singular variable-order time fractional Emden–Fowler equation generated by derivative with non-singular kernel |
| title_full_unstemmed | Shifted Jacobi polynomials for nonlinear singular variable-order time fractional Emden–Fowler equation generated by derivative with non-singular kernel |
| title_short | Shifted Jacobi polynomials for nonlinear singular variable-order time fractional Emden–Fowler equation generated by derivative with non-singular kernel |
| title_sort | shifted jacobi polynomials for nonlinear singular variable order time fractional emden fowler equation generated by derivative with non singular kernel |
| topic | Shifted Jacobi polynomials (SJPs) Operational matrices Variable-order (VO) time fractional derivative Singular VO time fractional Emden–Fowler equation |
| url | https://doi.org/10.1186/s13662-021-03349-1 |
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