Analytical Solution of Generalized Space-Time Fractional Advection-Dispersion Equation via Coupling of Sumudu and Fourier Transforms
The objective of this article is to present the computable solution of space-time advection-dispersion equation of fractional order associated with Hilfer-Prabhakar fractional derivative operator as well as fractional Laplace operator. The method followed in deriving the solution is that of joint Su...
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| Language: | English |
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Frontiers Media S.A.
2019-01-01
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| Series: | Frontiers in Physics |
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| Online Access: | https://www.frontiersin.org/article/10.3389/fphy.2018.00151/full |
| _version_ | 1819228909081722880 |
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| author | Vinod Gill Jagdev Singh Yudhveer Singh |
| author_facet | Vinod Gill Jagdev Singh Yudhveer Singh |
| author_sort | Vinod Gill |
| collection | DOAJ |
| description | The objective of this article is to present the computable solution of space-time advection-dispersion equation of fractional order associated with Hilfer-Prabhakar fractional derivative operator as well as fractional Laplace operator. The method followed in deriving the solution is that of joint Sumudu and Fourier transforms. The solution is derived in compact and graceful forms in terms of the generalized Mittag-Leffler function, which is suitable for numerical computation. Some illustration and special cases of main theorem are also discussed. |
| first_indexed | 2024-12-23T11:04:46Z |
| format | Article |
| id | doaj.art-4e482bfc44294053913b42d842eaeac9 |
| institution | Directory Open Access Journal |
| issn | 2296-424X |
| language | English |
| last_indexed | 2024-12-23T11:04:46Z |
| publishDate | 2019-01-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Physics |
| spelling | doaj.art-4e482bfc44294053913b42d842eaeac92022-12-21T17:49:31ZengFrontiers Media S.A.Frontiers in Physics2296-424X2019-01-01610.3389/fphy.2018.00151426623Analytical Solution of Generalized Space-Time Fractional Advection-Dispersion Equation via Coupling of Sumudu and Fourier TransformsVinod Gill0Jagdev Singh1Yudhveer Singh2Department of Mathematics, Government Post Graduate College Hisar, Hisar, IndiaDepartment of Mathematics, JECRC University, Jaipur, IndiaAmity Institute of Information Technology, Amity University, Jaipur, IndiaThe objective of this article is to present the computable solution of space-time advection-dispersion equation of fractional order associated with Hilfer-Prabhakar fractional derivative operator as well as fractional Laplace operator. The method followed in deriving the solution is that of joint Sumudu and Fourier transforms. The solution is derived in compact and graceful forms in terms of the generalized Mittag-Leffler function, which is suitable for numerical computation. Some illustration and special cases of main theorem are also discussed.https://www.frontiersin.org/article/10.3389/fphy.2018.00151/fullspace-time fractional advection-dispersion equationFourier transformsSumudu transformsHilfer-Prabhakar fractional derivativefractional laplacian operatorMittag-Leffler function |
| spellingShingle | Vinod Gill Jagdev Singh Yudhveer Singh Analytical Solution of Generalized Space-Time Fractional Advection-Dispersion Equation via Coupling of Sumudu and Fourier Transforms Frontiers in Physics space-time fractional advection-dispersion equation Fourier transforms Sumudu transforms Hilfer-Prabhakar fractional derivative fractional laplacian operator Mittag-Leffler function |
| title | Analytical Solution of Generalized Space-Time Fractional Advection-Dispersion Equation via Coupling of Sumudu and Fourier Transforms |
| title_full | Analytical Solution of Generalized Space-Time Fractional Advection-Dispersion Equation via Coupling of Sumudu and Fourier Transforms |
| title_fullStr | Analytical Solution of Generalized Space-Time Fractional Advection-Dispersion Equation via Coupling of Sumudu and Fourier Transforms |
| title_full_unstemmed | Analytical Solution of Generalized Space-Time Fractional Advection-Dispersion Equation via Coupling of Sumudu and Fourier Transforms |
| title_short | Analytical Solution of Generalized Space-Time Fractional Advection-Dispersion Equation via Coupling of Sumudu and Fourier Transforms |
| title_sort | analytical solution of generalized space time fractional advection dispersion equation via coupling of sumudu and fourier transforms |
| topic | space-time fractional advection-dispersion equation Fourier transforms Sumudu transforms Hilfer-Prabhakar fractional derivative fractional laplacian operator Mittag-Leffler function |
| url | https://www.frontiersin.org/article/10.3389/fphy.2018.00151/full |
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