Analysis of local fractional coupled Helmholtz and coupled Burgers' equations in fractal media
In this paper, we present a computational algorithm, namely, local fractional natural homotopy analysis method (LFNHAM) to explore the solutions of local fractional coupled Helmholtz and local fractional coupled Burgers' equations (LFCHEs and LFCBEs). This work also investigates the uniqueness...
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| Format: | Article |
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AIMS Press
2022-02-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2022450?viewType=HTML |
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| author | Ved Prakash Dubey Jagdev Singh Ahmed M. Alshehri Sarvesh Dubey Devendra Kumar |
| author_facet | Ved Prakash Dubey Jagdev Singh Ahmed M. Alshehri Sarvesh Dubey Devendra Kumar |
| author_sort | Ved Prakash Dubey |
| collection | DOAJ |
| description | In this paper, we present a computational algorithm, namely, local fractional natural homotopy analysis method (LFNHAM) to explore the solutions of local fractional coupled Helmholtz and local fractional coupled Burgers' equations (LFCHEs and LFCBEs). This work also investigates the uniqueness and convergence of the solution of a general local fractional partial differential equation (LFPDE) obtained by the suggested method in view of theory of fixed point and Banach spaces. Furthermore, the error analysis of the LFNHAM solution is also discussed. Moreover, the numerical simulations are presented for each of the local fractional coupled equations on the Cantor set. The computational procedure clearly illustrates the validity and reliability of the proposed method for achieving the solutions of local fractional coupled Helmholtz and coupled Burgers' equations. The proposed method also minimizes the computational work unlike other conventional methods while still giving extremely precise results. The implemented combination supplies a more general solution as compared to other methods and assimilates their consequences as a special case. In addition, the acquired solutions are also in excellent match with previously determined solutions. |
| first_indexed | 2024-12-19T22:37:26Z |
| format | Article |
| id | doaj.art-1a8d15d7ea8d410aaa07862e4fd9f402 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-19T22:37:26Z |
| publishDate | 2022-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-1a8d15d7ea8d410aaa07862e4fd9f4022022-12-21T20:03:09ZengAIMS PressAIMS Mathematics2473-69882022-02-01758080811110.3934/math.2022450Analysis of local fractional coupled Helmholtz and coupled Burgers' equations in fractal mediaVed Prakash Dubey 0Jagdev Singh 1Ahmed M. Alshehri2Sarvesh Dubey3Devendra Kumar41. Faculty of Mathematical and Statistical Sciences, Shri Ramswaroop Memorial University, Barabanki-225003, Uttar Pradesh, India2. Department of Mathematics, JECRC University, Jaipur-303905, Rajasthan, India 3. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Sciences, King Abdulaziz University, Jeddah, 21589, Saudi Arabia3. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Sciences, King Abdulaziz University, Jeddah, 21589, Saudi Arabia4. Department of Physics, L.N.D. College (B.R. Ambedkar Bihar University, Muzaffarpur), Motihari-845401, Bihar, India3. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Sciences, King Abdulaziz University, Jeddah, 21589, Saudi Arabia5. Department of Mathematics, University of Rajasthan, Jaipur-302004, Rajasthan, IndiaIn this paper, we present a computational algorithm, namely, local fractional natural homotopy analysis method (LFNHAM) to explore the solutions of local fractional coupled Helmholtz and local fractional coupled Burgers' equations (LFCHEs and LFCBEs). This work also investigates the uniqueness and convergence of the solution of a general local fractional partial differential equation (LFPDE) obtained by the suggested method in view of theory of fixed point and Banach spaces. Furthermore, the error analysis of the LFNHAM solution is also discussed. Moreover, the numerical simulations are presented for each of the local fractional coupled equations on the Cantor set. The computational procedure clearly illustrates the validity and reliability of the proposed method for achieving the solutions of local fractional coupled Helmholtz and coupled Burgers' equations. The proposed method also minimizes the computational work unlike other conventional methods while still giving extremely precise results. The implemented combination supplies a more general solution as compared to other methods and assimilates their consequences as a special case. In addition, the acquired solutions are also in excellent match with previously determined solutions.https://www.aimspress.com/article/doi/10.3934/math.2022450?viewType=HTMLlocal fractional coupled helmholtz equationslocal fractional coupled burgers' equationslocal fractional natural homotopy analysis methodlocal fractional derivativelocal fractional natural transform |
| spellingShingle | Ved Prakash Dubey Jagdev Singh Ahmed M. Alshehri Sarvesh Dubey Devendra Kumar Analysis of local fractional coupled Helmholtz and coupled Burgers' equations in fractal media AIMS Mathematics local fractional coupled helmholtz equations local fractional coupled burgers' equations local fractional natural homotopy analysis method local fractional derivative local fractional natural transform |
| title | Analysis of local fractional coupled Helmholtz and coupled Burgers' equations in fractal media |
| title_full | Analysis of local fractional coupled Helmholtz and coupled Burgers' equations in fractal media |
| title_fullStr | Analysis of local fractional coupled Helmholtz and coupled Burgers' equations in fractal media |
| title_full_unstemmed | Analysis of local fractional coupled Helmholtz and coupled Burgers' equations in fractal media |
| title_short | Analysis of local fractional coupled Helmholtz and coupled Burgers' equations in fractal media |
| title_sort | analysis of local fractional coupled helmholtz and coupled burgers equations in fractal media |
| topic | local fractional coupled helmholtz equations local fractional coupled burgers' equations local fractional natural homotopy analysis method local fractional derivative local fractional natural transform |
| url | https://www.aimspress.com/article/doi/10.3934/math.2022450?viewType=HTML |
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