A Novel Numerical Technique for Fractional Ordinary Differential Equations with Proportional Delay
Some researchers have combined two powerful techniques to establish a new method for solving fractional-order differential equations. In this study, we used a new combined technique, known as the Elzaki residual power series method (ERPSM), to offer approximate and exact solutions for fractional mul...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2022/6333084 |
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| author | Muhammad Imran Liaqat Adnan Khan Ali Akgül Md. Shajib Ali |
| author_facet | Muhammad Imran Liaqat Adnan Khan Ali Akgül Md. Shajib Ali |
| author_sort | Muhammad Imran Liaqat |
| collection | DOAJ |
| description | Some researchers have combined two powerful techniques to establish a new method for solving fractional-order differential equations. In this study, we used a new combined technique, known as the Elzaki residual power series method (ERPSM), to offer approximate and exact solutions for fractional multipantograph systems (FMPS) and pantograph differential equations (PDEs). In Caputo logic, the fractional-order derivative operator is measured. The Elzaki transform method and the residual power series method (RPSM) are combined in this novel technique. The suggested technique is based on a new version of Taylor’s series that generates a convergent series as a solution. Establishing the coefficients for a series, like the RPSM, necessitates computing the fractional derivatives each time. As ERPSM just requires the concept of a zero limit, we simply need a few computations to get the coefficients. The novel technique solves nonlinear problems without the need for He’s and Adomian polynomials, which is an advantage over the other combined methods based on homotopy perturbation and Adomian decomposition methods. The relative, recurrence, and absolute errors of the problems are analyzed to evaluate the efficiency and consistency of the presented method. Graphical significances are also identified for various values of fractional-order derivatives. As a result, the procedure is quick, precise, and easy to implement, and it yields outstanding results. |
| format | Article |
| id | doaj-art-286c5e60f1714606ad22d12467c6257e |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-286c5e60f1714606ad22d12467c6257e2025-02-03T01:32:32ZengWileyJournal of Function Spaces2314-88882022-01-01202210.1155/2022/6333084A Novel Numerical Technique for Fractional Ordinary Differential Equations with Proportional DelayMuhammad Imran Liaqat0Adnan Khan1Ali Akgül2Md. Shajib Ali3Department of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsSome researchers have combined two powerful techniques to establish a new method for solving fractional-order differential equations. In this study, we used a new combined technique, known as the Elzaki residual power series method (ERPSM), to offer approximate and exact solutions for fractional multipantograph systems (FMPS) and pantograph differential equations (PDEs). In Caputo logic, the fractional-order derivative operator is measured. The Elzaki transform method and the residual power series method (RPSM) are combined in this novel technique. The suggested technique is based on a new version of Taylor’s series that generates a convergent series as a solution. Establishing the coefficients for a series, like the RPSM, necessitates computing the fractional derivatives each time. As ERPSM just requires the concept of a zero limit, we simply need a few computations to get the coefficients. The novel technique solves nonlinear problems without the need for He’s and Adomian polynomials, which is an advantage over the other combined methods based on homotopy perturbation and Adomian decomposition methods. The relative, recurrence, and absolute errors of the problems are analyzed to evaluate the efficiency and consistency of the presented method. Graphical significances are also identified for various values of fractional-order derivatives. As a result, the procedure is quick, precise, and easy to implement, and it yields outstanding results.http://dx.doi.org/10.1155/2022/6333084 |
| spellingShingle | Muhammad Imran Liaqat Adnan Khan Ali Akgül Md. Shajib Ali A Novel Numerical Technique for Fractional Ordinary Differential Equations with Proportional Delay Journal of Function Spaces |
| title | A Novel Numerical Technique for Fractional Ordinary Differential Equations with Proportional Delay |
| title_full | A Novel Numerical Technique for Fractional Ordinary Differential Equations with Proportional Delay |
| title_fullStr | A Novel Numerical Technique for Fractional Ordinary Differential Equations with Proportional Delay |
| title_full_unstemmed | A Novel Numerical Technique for Fractional Ordinary Differential Equations with Proportional Delay |
| title_short | A Novel Numerical Technique for Fractional Ordinary Differential Equations with Proportional Delay |
| title_sort | novel numerical technique for fractional ordinary differential equations with proportional delay |
| url | http://dx.doi.org/10.1155/2022/6333084 |
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