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...

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Main Authors: Md. Asaduzzaman, Faruk Özger, Md. Zulfikar Ali
Format: Article
Language:English
Published: Elsevier 2024-12-01
Series:Partial Differential Equations in Applied Mathematics
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Online Access:http://www.sciencedirect.com/science/article/pii/S2666818124003231
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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.
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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