New approximate series solutions of conformable time–space fractional Fokker–Planck Equation via two efficacious techniques
This article presents a comparative analysis of the conformable time–space fractional Fokker–Planck equation (TSF-FP equation) by operating two efficacious techniques: Fractional homotopy analysis transform method (FHATM) and conformable homotopy transform method (CHTM). The efficaciousness and vali...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Elsevier
2022-12-01
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| Series: | Partial Differential Equations in Applied Mathematics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818122000997 |
| _version_ | 1811201499071512576 |
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| author | Brajesh Kumar Singh Anil Kumar |
| author_facet | Brajesh Kumar Singh Anil Kumar |
| author_sort | Brajesh Kumar Singh |
| collection | DOAJ |
| description | This article presents a comparative analysis of the conformable time–space fractional Fokker–Planck equation (TSF-FP equation) by operating two efficacious techniques: Fractional homotopy analysis transform method (FHATM) and conformable homotopy transform method (CHTM). The efficaciousness and validity of the proposed techniques are represented in terms of three different examples of conformable TSF-FP equations by computing various error norms: L2and absolute error. Convergence analysis of both techniques are studied theocratically and verified graphically as well. The findings demonstrate that for a given order of approximation CHTM requires less computational time in comparison to FHATM while FHATM is more general and converges faster than CHTM. The obtained information is confirmed graphically for different numerical values of fractional order. |
| first_indexed | 2024-04-12T02:22:40Z |
| format | Article |
| id | doaj.art-bc9e54f8c47c45ec92f9fb4ee16ab09b |
| institution | Directory Open Access Journal |
| issn | 2666-8181 |
| language | English |
| last_indexed | 2024-04-12T02:22:40Z |
| publishDate | 2022-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj.art-bc9e54f8c47c45ec92f9fb4ee16ab09b2022-12-22T03:52:05ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812022-12-016100451New approximate series solutions of conformable time–space fractional Fokker–Planck Equation via two efficacious techniquesBrajesh Kumar Singh0Anil Kumar1Corresponding author.; School of Physical and Decision Sciences, Department of Mathematics, Babasaheb Bhimrao Ambedkar University, Lucknow 226025, UP, IndiaSchool of Physical and Decision Sciences, Department of Mathematics, Babasaheb Bhimrao Ambedkar University, Lucknow 226025, UP, IndiaThis article presents a comparative analysis of the conformable time–space fractional Fokker–Planck equation (TSF-FP equation) by operating two efficacious techniques: Fractional homotopy analysis transform method (FHATM) and conformable homotopy transform method (CHTM). The efficaciousness and validity of the proposed techniques are represented in terms of three different examples of conformable TSF-FP equations by computing various error norms: L2and absolute error. Convergence analysis of both techniques are studied theocratically and verified graphically as well. The findings demonstrate that for a given order of approximation CHTM requires less computational time in comparison to FHATM while FHATM is more general and converges faster than CHTM. The obtained information is confirmed graphically for different numerical values of fractional order.http://www.sciencedirect.com/science/article/pii/S2666818122000997Fractional homotopy analysis transform method (FHATM)Conformable homotopy transform method (CHTM)Conformable TSF-Fokker–Planck equationConvergenceConformable fractional derivative (Co-FD) |
| spellingShingle | Brajesh Kumar Singh Anil Kumar New approximate series solutions of conformable time–space fractional Fokker–Planck Equation via two efficacious techniques Partial Differential Equations in Applied Mathematics Fractional homotopy analysis transform method (FHATM) Conformable homotopy transform method (CHTM) Conformable TSF-Fokker–Planck equation Convergence Conformable fractional derivative (Co-FD) |
| title | New approximate series solutions of conformable time–space fractional Fokker–Planck Equation via two efficacious techniques |
| title_full | New approximate series solutions of conformable time–space fractional Fokker–Planck Equation via two efficacious techniques |
| title_fullStr | New approximate series solutions of conformable time–space fractional Fokker–Planck Equation via two efficacious techniques |
| title_full_unstemmed | New approximate series solutions of conformable time–space fractional Fokker–Planck Equation via two efficacious techniques |
| title_short | New approximate series solutions of conformable time–space fractional Fokker–Planck Equation via two efficacious techniques |
| title_sort | new approximate series solutions of conformable time space fractional fokker planck equation via two efficacious techniques |
| topic | Fractional homotopy analysis transform method (FHATM) Conformable homotopy transform method (CHTM) Conformable TSF-Fokker–Planck equation Convergence Conformable fractional derivative (Co-FD) |
| url | http://www.sciencedirect.com/science/article/pii/S2666818122000997 |
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