Modified wavelets–based algorithm for nonlinear delay differential equations of fractional order
Most of the physical phenomena located around us are nonlinear in nature and their solutions are of great significance for scientists and engineers. In order to have a better representation of these physical phenomena, fractional calculus is developed. Some of these nonlinear physical models can be...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SAGE Publishing
2017-04-01
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| Series: | Advances in Mechanical Engineering |
| Online Access: | https://doi.org/10.1177/1687814017696223 |
| _version_ | 1819260466635997184 |
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| author | Muhammad Asad Iqbal Muhammad Shakeel Syed Tauseef Mohyud-Din Muhammad Rafiq |
| author_facet | Muhammad Asad Iqbal Muhammad Shakeel Syed Tauseef Mohyud-Din Muhammad Rafiq |
| author_sort | Muhammad Asad Iqbal |
| collection | DOAJ |
| description | Most of the physical phenomena located around us are nonlinear in nature and their solutions are of great significance for scientists and engineers. In order to have a better representation of these physical phenomena, fractional calculus is developed. Some of these nonlinear physical models can be represented in the form of delay differential equations of fractional order. In this article, a new method named Gegenbauer Wavelets Steps Method is proposed using Gegenbauer polynomials and method of steps for solving nonlinear fractional delay differential equations. Method of steps is used to convert the fractional nonlinear fractional delay differential equation into a fractional nonlinear differential equation and then Gegenbauer wavelet method is applied at each iteration of fractional differential equation to find the solution. To check the accuracy and efficiency of the proposed method, the proposed method is implemented on different nonlinear fractional delay differential equations including singular-type problems also. |
| first_indexed | 2024-12-23T19:26:21Z |
| format | Article |
| id | doaj.art-be5a90d0bef54c16815c05a326625411 |
| institution | Directory Open Access Journal |
| issn | 1687-8140 |
| language | English |
| last_indexed | 2024-12-23T19:26:21Z |
| publishDate | 2017-04-01 |
| publisher | SAGE Publishing |
| record_format | Article |
| series | Advances in Mechanical Engineering |
| spelling | doaj.art-be5a90d0bef54c16815c05a3266254112022-12-21T17:34:02ZengSAGE PublishingAdvances in Mechanical Engineering1687-81402017-04-01910.1177/1687814017696223Modified wavelets–based algorithm for nonlinear delay differential equations of fractional orderMuhammad Asad Iqbal0Muhammad Shakeel1Syed Tauseef Mohyud-Din2Muhammad Rafiq3Department of Mathematics, Mohi-Ud-Din Islamic University, Nerian Sharif AJK, PakistanDepartment of Mathematics, Mohi-Ud-Din Islamic University, Nerian Sharif AJK, PakistanDepartment of Mathematics, Faculty of Sciences, HITEC University, Taxila, PakistanDepartment of Mathematics, COMSATS Institute of Information Technology, Wah Cantt, PakistanMost of the physical phenomena located around us are nonlinear in nature and their solutions are of great significance for scientists and engineers. In order to have a better representation of these physical phenomena, fractional calculus is developed. Some of these nonlinear physical models can be represented in the form of delay differential equations of fractional order. In this article, a new method named Gegenbauer Wavelets Steps Method is proposed using Gegenbauer polynomials and method of steps for solving nonlinear fractional delay differential equations. Method of steps is used to convert the fractional nonlinear fractional delay differential equation into a fractional nonlinear differential equation and then Gegenbauer wavelet method is applied at each iteration of fractional differential equation to find the solution. To check the accuracy and efficiency of the proposed method, the proposed method is implemented on different nonlinear fractional delay differential equations including singular-type problems also.https://doi.org/10.1177/1687814017696223 |
| spellingShingle | Muhammad Asad Iqbal Muhammad Shakeel Syed Tauseef Mohyud-Din Muhammad Rafiq Modified wavelets–based algorithm for nonlinear delay differential equations of fractional order Advances in Mechanical Engineering |
| title | Modified wavelets–based algorithm for nonlinear delay differential equations of fractional order |
| title_full | Modified wavelets–based algorithm for nonlinear delay differential equations of fractional order |
| title_fullStr | Modified wavelets–based algorithm for nonlinear delay differential equations of fractional order |
| title_full_unstemmed | Modified wavelets–based algorithm for nonlinear delay differential equations of fractional order |
| title_short | Modified wavelets–based algorithm for nonlinear delay differential equations of fractional order |
| title_sort | modified wavelets based algorithm for nonlinear delay differential equations of fractional order |
| url | https://doi.org/10.1177/1687814017696223 |
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