Fibonacci wavelet method for the numerical solution of a fractional relaxation–oscillation model
In this paper, we have discussed the Fibonacci wavelet (FW) framework for numerical simulations of the fractional relaxation–oscillation model (FROM). Firstly, the fractional order operational matrices of integration associated with the FW are constructed via the block pulse functions. The operation...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2023-12-01
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| Series: | Partial Differential Equations in Applied Mathematics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818123000815 |
| _version_ | 1797390346351542272 |
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| author | Shah Jahan Shahid Ahmed Pooja Yadav Kottakkaran Sooppy Nisar |
| author_facet | Shah Jahan Shahid Ahmed Pooja Yadav Kottakkaran Sooppy Nisar |
| author_sort | Shah Jahan |
| collection | DOAJ |
| description | In this paper, we have discussed the Fibonacci wavelet (FW) framework for numerical simulations of the fractional relaxation–oscillation model (FROM). Firstly, the fractional order operational matrices of integration associated with the FW are constructed via the block pulse functions. The operational matrices merged with the collocation method are used to convert the given problem into a system of algebraic equations that is solved by the Newton method. We conduct error analysis, perform numerical simulations, and present the corresponding results to establish the credibility and practical applicability of the proposed technique. Numerical examples are provided to show the efficiency of our approach. To show the accuracy of the FW-based numerical technique, the approximate solutions of FROM are compared with the exact solution and other existing methods. This research opens up new possibilities for using FW as a powerful tool for addressing complex mathematical problems in real-world systems. |
| first_indexed | 2024-03-08T23:10:23Z |
| format | Article |
| id | doaj.art-68ecf14541e54a55b75278bcf2d06b3f |
| institution | Directory Open Access Journal |
| issn | 2666-8181 |
| language | English |
| last_indexed | 2024-03-08T23:10:23Z |
| publishDate | 2023-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj.art-68ecf14541e54a55b75278bcf2d06b3f2023-12-15T07:26:49ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812023-12-018100568Fibonacci wavelet method for the numerical solution of a fractional relaxation–oscillation modelShah Jahan0Shahid Ahmed1Pooja Yadav2Kottakkaran Sooppy Nisar3Department of Mathematics, Central University of Haryana, Mahendergarh 123029, IndiaDepartment of Mathematics, Central University of Haryana, Mahendergarh 123029, IndiaDepartment of Mathematics, Central University of Haryana, Mahendergarh 123029, IndiaDepartment of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam Bin Abdulaziz University, Kingdom of Saudi Arabia; Corresponding author.In this paper, we have discussed the Fibonacci wavelet (FW) framework for numerical simulations of the fractional relaxation–oscillation model (FROM). Firstly, the fractional order operational matrices of integration associated with the FW are constructed via the block pulse functions. The operational matrices merged with the collocation method are used to convert the given problem into a system of algebraic equations that is solved by the Newton method. We conduct error analysis, perform numerical simulations, and present the corresponding results to establish the credibility and practical applicability of the proposed technique. Numerical examples are provided to show the efficiency of our approach. To show the accuracy of the FW-based numerical technique, the approximate solutions of FROM are compared with the exact solution and other existing methods. This research opens up new possibilities for using FW as a powerful tool for addressing complex mathematical problems in real-world systems.http://www.sciencedirect.com/science/article/pii/S2666818123000815Fibonacci waveletFractional calculusOperational matricesViscoelasticityRelaxation–oscillation equations |
| spellingShingle | Shah Jahan Shahid Ahmed Pooja Yadav Kottakkaran Sooppy Nisar Fibonacci wavelet method for the numerical solution of a fractional relaxation–oscillation model Partial Differential Equations in Applied Mathematics Fibonacci wavelet Fractional calculus Operational matrices Viscoelasticity Relaxation–oscillation equations |
| title | Fibonacci wavelet method for the numerical solution of a fractional relaxation–oscillation model |
| title_full | Fibonacci wavelet method for the numerical solution of a fractional relaxation–oscillation model |
| title_fullStr | Fibonacci wavelet method for the numerical solution of a fractional relaxation–oscillation model |
| title_full_unstemmed | Fibonacci wavelet method for the numerical solution of a fractional relaxation–oscillation model |
| title_short | Fibonacci wavelet method for the numerical solution of a fractional relaxation–oscillation model |
| title_sort | fibonacci wavelet method for the numerical solution of a fractional relaxation oscillation model |
| topic | Fibonacci wavelet Fractional calculus Operational matrices Viscoelasticity Relaxation–oscillation equations |
| url | http://www.sciencedirect.com/science/article/pii/S2666818123000815 |
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