The Fractional Investigation of Some Dynamical Systems With Caputo Operator
In the present work, an Elzaki transformation is combined with a decomposition technique for the solutions of fractional dynamical systems. The targeted problems are related to the systems of fractional partial differential equations. Fractional differential equations are useful for more accurate mo...
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| Language: | English |
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Frontiers Media S.A.
2022-05-01
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| Series: | Frontiers in Physics |
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| Online Access: | https://www.frontiersin.org/articles/10.3389/fphy.2022.895451/full |
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| author | Qasim Khan Hassan Khan Hassan Khan Poom Kumam Poom Kumam Hajira Kanokwan Sitthithakerngkiet |
| author_facet | Qasim Khan Hassan Khan Hassan Khan Poom Kumam Poom Kumam Hajira Kanokwan Sitthithakerngkiet |
| author_sort | Qasim Khan |
| collection | DOAJ |
| description | In the present work, an Elzaki transformation is combined with a decomposition technique for the solutions of fractional dynamical systems. The targeted problems are related to the systems of fractional partial differential equations. Fractional differential equations are useful for more accurate modeling of various phenomena. The Elzaki transform decomposition method is implemented in a very simple and straightforward manner to solve the suggested problems. The proposed technique requires fewer calculations and needs no discretization or parametrization. The derivative of fractional order is represented in a Caputo form. To show the conclusion, which is drawn from the results, some numerical examples are considered for their approximate analytical solution. The series solutions to the targeted problems are obtained having components with a greater rate of convergence toward the exact solutions. The new results are represented by using tables and graphs, which show the sufficient accuracy of the present method as compared to other existing techniques. It is shown through graphs and tables that the actual and approximate results are very close to each other, which shows the applicability of the presented method. The fractional-order solutions are in best agreement with the dynamics of the given problems and provide infinite choices for an optimal solution to the suggested mathematical model. The novelty of the present work is that it applies an efficient procedure with less computational cost and attains a higher degree of accuracy. Furthermore, the proposed technique can be used to solve other nonlinear fractional problems in the future, which will be a scientific contribution to research society. |
| first_indexed | 2024-04-12T11:14:38Z |
| format | Article |
| id | doaj.art-62578552f2a64d9caf763ffebd79229b |
| institution | Directory Open Access Journal |
| issn | 2296-424X |
| language | English |
| last_indexed | 2024-04-12T11:14:38Z |
| publishDate | 2022-05-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Physics |
| spelling | doaj.art-62578552f2a64d9caf763ffebd79229b2022-12-22T03:35:32ZengFrontiers Media S.A.Frontiers in Physics2296-424X2022-05-011010.3389/fphy.2022.895451895451The Fractional Investigation of Some Dynamical Systems With Caputo OperatorQasim Khan0Hassan Khan1Hassan Khan2Poom Kumam3Poom Kumam4 Hajira5Kanokwan Sitthithakerngkiet6Department of Mathematics, Abdul Wali Khan Uniuersity Mardan, Mardan, PakistanDepartment of Mathematics, Abdul Wali Khan Uniuersity Mardan, Mardan, PakistanDepartment of Mathematics, Near East University TRNC, Mersin, TurkeyDepartment of Medical Research, China Medical University Hospital, China Medical University, Taichung, TaiwanDepartment of Mathematics, Theoretical and Computational Science (TaCS) Center, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bangkok, ThailandDepartment of Mathematics, Abdul Wali Khan Uniuersity Mardan, Mardan, PakistanIntelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok (KMUTNB), Bangkok, ThailandIn the present work, an Elzaki transformation is combined with a decomposition technique for the solutions of fractional dynamical systems. The targeted problems are related to the systems of fractional partial differential equations. Fractional differential equations are useful for more accurate modeling of various phenomena. The Elzaki transform decomposition method is implemented in a very simple and straightforward manner to solve the suggested problems. The proposed technique requires fewer calculations and needs no discretization or parametrization. The derivative of fractional order is represented in a Caputo form. To show the conclusion, which is drawn from the results, some numerical examples are considered for their approximate analytical solution. The series solutions to the targeted problems are obtained having components with a greater rate of convergence toward the exact solutions. The new results are represented by using tables and graphs, which show the sufficient accuracy of the present method as compared to other existing techniques. It is shown through graphs and tables that the actual and approximate results are very close to each other, which shows the applicability of the presented method. The fractional-order solutions are in best agreement with the dynamics of the given problems and provide infinite choices for an optimal solution to the suggested mathematical model. The novelty of the present work is that it applies an efficient procedure with less computational cost and attains a higher degree of accuracy. Furthermore, the proposed technique can be used to solve other nonlinear fractional problems in the future, which will be a scientific contribution to research society.https://www.frontiersin.org/articles/10.3389/fphy.2022.895451/fullElzaki transformationdecomposition methodnonlinear fractional partial differential equationsanalytical methodnonlinear systemsabsolute error |
| spellingShingle | Qasim Khan Hassan Khan Hassan Khan Poom Kumam Poom Kumam Hajira Kanokwan Sitthithakerngkiet The Fractional Investigation of Some Dynamical Systems With Caputo Operator Frontiers in Physics Elzaki transformation decomposition method nonlinear fractional partial differential equations analytical method nonlinear systems absolute error |
| title | The Fractional Investigation of Some Dynamical Systems With Caputo Operator |
| title_full | The Fractional Investigation of Some Dynamical Systems With Caputo Operator |
| title_fullStr | The Fractional Investigation of Some Dynamical Systems With Caputo Operator |
| title_full_unstemmed | The Fractional Investigation of Some Dynamical Systems With Caputo Operator |
| title_short | The Fractional Investigation of Some Dynamical Systems With Caputo Operator |
| title_sort | fractional investigation of some dynamical systems with caputo operator |
| topic | Elzaki transformation decomposition method nonlinear fractional partial differential equations analytical method nonlinear systems absolute error |
| url | https://www.frontiersin.org/articles/10.3389/fphy.2022.895451/full |
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