Analytical approximate solutions of some fractional nonlinear evolution equations through AFVI method
In this article, we construct and investigate a new fractional variational iteration technique which is named as AFVI method. After that, we formulate some IVPs corresponding to the fractional nonlinear evolution equations NLTFFWE, mNLTFFWE, TFmCHE and TFmDPE. The Caputo fractional order derivative...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2024-12-01
|
| Series: | Partial Differential Equations in Applied Mathematics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818124003231 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850245196498862080 |
|---|---|
| author | Md. Asaduzzaman Faruk Özger Md. Zulfikar Ali |
| author_facet | Md. Asaduzzaman Faruk Özger Md. Zulfikar Ali |
| author_sort | Md. Asaduzzaman |
| collection | DOAJ |
| description | In this article, we construct and investigate a new fractional variational iteration technique which is named as AFVI method. After that, we formulate some IVPs corresponding to the fractional nonlinear evolution equations NLTFFWE, mNLTFFWE, TFmCHE and TFmDPE. The Caputo fractional order derivative has been used to fractionalize the considered NLEEs. Then, we solve the considered IVPs by applying the formulated AFVI method. Lastly, we check the accuracy of the attained AASs by making some graphical and numerical comparisons with their corresponding exact solutions and other existing equivalent AASs. The result of this article confirm that the efficiency, appropriateness and time spent capability of the newly constructed AFVI method are better than that of the other existing analogous fractional analytical approximation methods. Here, we apply the Maple 2021 programming software to obtain the AASs of the formulated IVPs and drawing the 3D graphs of the attained AASs. Finally, in this article we validate the applicability of the Caputo fractional order derivative to form a novel analytical approximation method as well as to fractionalize some essential NLEEs of Mathematical physics. |
| format | Article |
| id | doaj-art-c769c4a477c74fcfb6259b2af2379d97 |
| institution | OA Journals |
| issn | 2666-8181 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj-art-c769c4a477c74fcfb6259b2af2379d972025-08-20T01:59:31ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812024-12-011210093710.1016/j.padiff.2024.100937Analytical approximate solutions of some fractional nonlinear evolution equations through AFVI methodMd. Asaduzzaman0Faruk Özger1Md. Zulfikar Ali2Department of Mathematics, Islamic University, Kushtia, 7003, Bangladesh; Corresponding author. Md. AsaduzzamanDepartment of Computer Engineering, Şehit Bülent Yurtseven Campus, Iğdır University, 76000 Iğdır, TürkiyeDepartment of Mathematics, University of Rajshahi, Rajshahi, 6205, BangladeshIn this article, we construct and investigate a new fractional variational iteration technique which is named as AFVI method. After that, we formulate some IVPs corresponding to the fractional nonlinear evolution equations NLTFFWE, mNLTFFWE, TFmCHE and TFmDPE. The Caputo fractional order derivative has been used to fractionalize the considered NLEEs. Then, we solve the considered IVPs by applying the formulated AFVI method. Lastly, we check the accuracy of the attained AASs by making some graphical and numerical comparisons with their corresponding exact solutions and other existing equivalent AASs. The result of this article confirm that the efficiency, appropriateness and time spent capability of the newly constructed AFVI method are better than that of the other existing analogous fractional analytical approximation methods. Here, we apply the Maple 2021 programming software to obtain the AASs of the formulated IVPs and drawing the 3D graphs of the attained AASs. Finally, in this article we validate the applicability of the Caputo fractional order derivative to form a novel analytical approximation method as well as to fractionalize some essential NLEEs of Mathematical physics.http://www.sciencedirect.com/science/article/pii/S2666818124003231AFVI methodFractional nonlinear evolution equationsCaputo fractional order derivativeAnalytical approximate solutionConvergence analysis |
| spellingShingle | Md. Asaduzzaman Faruk Özger Md. Zulfikar Ali Analytical approximate solutions of some fractional nonlinear evolution equations through AFVI method Partial Differential Equations in Applied Mathematics AFVI method Fractional nonlinear evolution equations Caputo fractional order derivative Analytical approximate solution Convergence analysis |
| title | Analytical approximate solutions of some fractional nonlinear evolution equations through AFVI method |
| title_full | Analytical approximate solutions of some fractional nonlinear evolution equations through AFVI method |
| title_fullStr | Analytical approximate solutions of some fractional nonlinear evolution equations through AFVI method |
| title_full_unstemmed | Analytical approximate solutions of some fractional nonlinear evolution equations through AFVI method |
| title_short | Analytical approximate solutions of some fractional nonlinear evolution equations through AFVI method |
| title_sort | analytical approximate solutions of some fractional nonlinear evolution equations through afvi method |
| topic | AFVI method Fractional nonlinear evolution equations Caputo fractional order derivative Analytical approximate solution Convergence analysis |
| url | http://www.sciencedirect.com/science/article/pii/S2666818124003231 |
| work_keys_str_mv | AT mdasaduzzaman analyticalapproximatesolutionsofsomefractionalnonlinearevolutionequationsthroughafvimethod AT farukozger analyticalapproximatesolutionsofsomefractionalnonlinearevolutionequationsthroughafvimethod AT mdzulfikarali analyticalapproximatesolutionsofsomefractionalnonlinearevolutionequationsthroughafvimethod |