A Numerical Computation for an Impulsive Fractional Differential Equation with a Deviated Argument
Symmetry analysis is an effective tool for understanding differential equations, particularly when analyzing equations derived from mathematical concepts. This paper is concerned with an impulsive fractional differential equation (IFDE) with a deviated argument. We implement two techniques, the Adom...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-11-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/11/2404 |
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| author | Ebrahem A. Algehyne Areefa Khatoon Abdur Raheem Ahmed Alamer |
| author_facet | Ebrahem A. Algehyne Areefa Khatoon Abdur Raheem Ahmed Alamer |
| author_sort | Ebrahem A. Algehyne |
| collection | DOAJ |
| description | Symmetry analysis is an effective tool for understanding differential equations, particularly when analyzing equations derived from mathematical concepts. This paper is concerned with an impulsive fractional differential equation (IFDE) with a deviated argument. We implement two techniques, the Adomian decomposition method (ADM) and the fractional differential transform method (FDTM), for solving IFDEs. In these schemes, we obtain the solutions in the form of a convergent power series with easily computed components. This paper also discusses the existence and uniqueness of solutions using the Banach contraction principle. This paper presents a numerical comparison between the two methods for solving IFDEs. We illustrate the proposed methods with a few examples and find their numerical solutions. Moreover, we show the graph of numerical solutions via MATLAB. The numerical results demonstrate that the ADM approach is quite accurate and readily implemented. |
| first_indexed | 2024-03-09T17:57:03Z |
| format | Article |
| id | doaj.art-4bea1ba6ebe642118730336b63dc8ba3 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T17:57:03Z |
| publishDate | 2022-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-4bea1ba6ebe642118730336b63dc8ba32023-11-24T10:13:29ZengMDPI AGSymmetry2073-89942022-11-011411240410.3390/sym14112404A Numerical Computation for an Impulsive Fractional Differential Equation with a Deviated ArgumentEbrahem A. Algehyne0Areefa Khatoon1Abdur Raheem2Ahmed Alamer3Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi ArabiaDepartment of Mathematics, Aligarh Muslim University, Aligarh 202002, IndiaDepartment of Mathematics, Aligarh Muslim University, Aligarh 202002, IndiaDepartment of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi ArabiaSymmetry analysis is an effective tool for understanding differential equations, particularly when analyzing equations derived from mathematical concepts. This paper is concerned with an impulsive fractional differential equation (IFDE) with a deviated argument. We implement two techniques, the Adomian decomposition method (ADM) and the fractional differential transform method (FDTM), for solving IFDEs. In these schemes, we obtain the solutions in the form of a convergent power series with easily computed components. This paper also discusses the existence and uniqueness of solutions using the Banach contraction principle. This paper presents a numerical comparison between the two methods for solving IFDEs. We illustrate the proposed methods with a few examples and find their numerical solutions. Moreover, we show the graph of numerical solutions via MATLAB. The numerical results demonstrate that the ADM approach is quite accurate and readily implemented.https://www.mdpi.com/2073-8994/14/11/2404Adomian decomposition methodfractional differential transformCaputo fractional derivativeimpulsedeviated argumentsnumerical solutions |
| spellingShingle | Ebrahem A. Algehyne Areefa Khatoon Abdur Raheem Ahmed Alamer A Numerical Computation for an Impulsive Fractional Differential Equation with a Deviated Argument Symmetry Adomian decomposition method fractional differential transform Caputo fractional derivative impulse deviated arguments numerical solutions |
| title | A Numerical Computation for an Impulsive Fractional Differential Equation with a Deviated Argument |
| title_full | A Numerical Computation for an Impulsive Fractional Differential Equation with a Deviated Argument |
| title_fullStr | A Numerical Computation for an Impulsive Fractional Differential Equation with a Deviated Argument |
| title_full_unstemmed | A Numerical Computation for an Impulsive Fractional Differential Equation with a Deviated Argument |
| title_short | A Numerical Computation for an Impulsive Fractional Differential Equation with a Deviated Argument |
| title_sort | numerical computation for an impulsive fractional differential equation with a deviated argument |
| topic | Adomian decomposition method fractional differential transform Caputo fractional derivative impulse deviated arguments numerical solutions |
| url | https://www.mdpi.com/2073-8994/14/11/2404 |
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