An Innovative Analytical Approach for the Solution of Fractional Differential Equations Using the Integral Transform
In this study, we suggest a straightforward analytical/semi-analytical method based on the Elzaki transform (ET) method to find the solution to a number of differential fractional boundary value problems with initial conditions (ICs). The suggested approach not only resolves the issue of some equati...
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MDPI AG
2025-05-01
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| Online Access: | https://www.mdpi.com/2075-1680/14/5/363 |
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| author | Eltaib M. Abd Elmohmoud Tarig M. Elzaki |
| author_facet | Eltaib M. Abd Elmohmoud Tarig M. Elzaki |
| author_sort | Eltaib M. Abd Elmohmoud |
| collection | DOAJ |
| description | In this study, we suggest a straightforward analytical/semi-analytical method based on the Elzaki transform (ET) method to find the solution to a number of differential fractional boundary value problems with initial conditions (ICs). The suggested approach not only resolves the issue of some equation nonlinearity but also transforms the issue into a simpler algebraic recurrence problem. In science and engineering, fractional differential equations (FDEs) can be solved with the help of this basic but effective concept. Some illustrative cases are used to demonstrate the efficacy and value of the suggested technique. |
| format | Article |
| id | doaj-art-c60d48cce29c413d8c0b809fa9ca0cdc |
| institution | OA Journals |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-c60d48cce29c413d8c0b809fa9ca0cdc2025-08-20T02:33:39ZengMDPI AGAxioms2075-16802025-05-0114536310.3390/axioms14050363An Innovative Analytical Approach for the Solution of Fractional Differential Equations Using the Integral TransformEltaib M. Abd Elmohmoud0Tarig M. Elzaki1Mathematics Department, University of Jeddah, Jeddah 23218, Saudi ArabiaMathematics Department, University of Jeddah, Jeddah 23218, Saudi ArabiaIn this study, we suggest a straightforward analytical/semi-analytical method based on the Elzaki transform (ET) method to find the solution to a number of differential fractional boundary value problems with initial conditions (ICs). The suggested approach not only resolves the issue of some equation nonlinearity but also transforms the issue into a simpler algebraic recurrence problem. In science and engineering, fractional differential equations (FDEs) can be solved with the help of this basic but effective concept. Some illustrative cases are used to demonstrate the efficacy and value of the suggested technique.https://www.mdpi.com/2075-1680/14/5/363fractional differential equationsintegral transformMittag–Leffler |
| spellingShingle | Eltaib M. Abd Elmohmoud Tarig M. Elzaki An Innovative Analytical Approach for the Solution of Fractional Differential Equations Using the Integral Transform Axioms fractional differential equations integral transform Mittag–Leffler |
| title | An Innovative Analytical Approach for the Solution of Fractional Differential Equations Using the Integral Transform |
| title_full | An Innovative Analytical Approach for the Solution of Fractional Differential Equations Using the Integral Transform |
| title_fullStr | An Innovative Analytical Approach for the Solution of Fractional Differential Equations Using the Integral Transform |
| title_full_unstemmed | An Innovative Analytical Approach for the Solution of Fractional Differential Equations Using the Integral Transform |
| title_short | An Innovative Analytical Approach for the Solution of Fractional Differential Equations Using the Integral Transform |
| title_sort | innovative analytical approach for the solution of fractional differential equations using the integral transform |
| topic | fractional differential equations integral transform Mittag–Leffler |
| url | https://www.mdpi.com/2075-1680/14/5/363 |
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