Analytical Investigation of Some Dynamical Systems by ZZ Transform with Mittag–Leffler Kernel
In this work, ZZ transformation is combined with the Adomian decomposition method to solve the dynamical system of fractional order. The derivative of fractional order is represented in the Atangana–Baleanu derivative. The numerical examples are combined for their approximate-analytical solution. It...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2022/7635696 |
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| _version_ | 1832549713436475392 |
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| author | Mounirah Areshi Muhammad Naeem Noorolhuda Wyal |
| author_facet | Mounirah Areshi Muhammad Naeem Noorolhuda Wyal |
| author_sort | Mounirah Areshi |
| collection | DOAJ |
| description | In this work, ZZ transformation is combined with the Adomian decomposition method to solve the dynamical system of fractional order. The derivative of fractional order is represented in the Atangana–Baleanu derivative. The numerical examples are combined for their approximate-analytical solution. It is explored using graphs that indicate that the actual and approximation results are close to each other, demonstrating the method’s usefulness. Fractional-order solutions are the most in line with the dynamics of the targeted problems, and they provide an endless number of options for an optimal mathematical model solution for a particular physical phenomenon. This analytical approach produces a series form solution that is quickly convergent to exact solutions. The acquired results suggest that the novel analytical solution technique is simple to use and very successful at assessing complicated problems that arise in related fields of research and technology. |
| format | Article |
| id | doaj-art-533fafac4fce45f09bab968d7777715c |
| institution | Kabale University |
| issn | 1099-0526 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-533fafac4fce45f09bab968d7777715c2025-02-03T06:08:46ZengWileyComplexity1099-05262022-01-01202210.1155/2022/7635696Analytical Investigation of Some Dynamical Systems by ZZ Transform with Mittag–Leffler KernelMounirah Areshi0Muhammad Naeem1Noorolhuda Wyal2Department of MathematicsDeanship of Joint First Year Umm Al-Qura University MakkahDepartment of MathematicsIn this work, ZZ transformation is combined with the Adomian decomposition method to solve the dynamical system of fractional order. The derivative of fractional order is represented in the Atangana–Baleanu derivative. The numerical examples are combined for their approximate-analytical solution. It is explored using graphs that indicate that the actual and approximation results are close to each other, demonstrating the method’s usefulness. Fractional-order solutions are the most in line with the dynamics of the targeted problems, and they provide an endless number of options for an optimal mathematical model solution for a particular physical phenomenon. This analytical approach produces a series form solution that is quickly convergent to exact solutions. The acquired results suggest that the novel analytical solution technique is simple to use and very successful at assessing complicated problems that arise in related fields of research and technology.http://dx.doi.org/10.1155/2022/7635696 |
| spellingShingle | Mounirah Areshi Muhammad Naeem Noorolhuda Wyal Analytical Investigation of Some Dynamical Systems by ZZ Transform with Mittag–Leffler Kernel Complexity |
| title | Analytical Investigation of Some Dynamical Systems by ZZ Transform with Mittag–Leffler Kernel |
| title_full | Analytical Investigation of Some Dynamical Systems by ZZ Transform with Mittag–Leffler Kernel |
| title_fullStr | Analytical Investigation of Some Dynamical Systems by ZZ Transform with Mittag–Leffler Kernel |
| title_full_unstemmed | Analytical Investigation of Some Dynamical Systems by ZZ Transform with Mittag–Leffler Kernel |
| title_short | Analytical Investigation of Some Dynamical Systems by ZZ Transform with Mittag–Leffler Kernel |
| title_sort | analytical investigation of some dynamical systems by zz transform with mittag leffler kernel |
| url | http://dx.doi.org/10.1155/2022/7635696 |
| work_keys_str_mv | AT mounirahareshi analyticalinvestigationofsomedynamicalsystemsbyzztransformwithmittaglefflerkernel AT muhammadnaeem analyticalinvestigationofsomedynamicalsystemsbyzztransformwithmittaglefflerkernel AT noorolhudawyal analyticalinvestigationofsomedynamicalsystemsbyzztransformwithmittaglefflerkernel |