Iterative Procedure for Non-Linear Fractional Integro-Differential Equations via Daftardar--Jafari Polynomials
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913693154934784 |
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| author | Khan, Qasim Suen, Anthony |
| author_facet | Khan, Qasim Suen, Anthony |
| contents | In this paper, we introduce a novel approach called the Iterative Aboodh Transform Method (IATM) which utilizes Daftardar--Jafari polynomials for solving non-linear problems. Such method is employed to derive solutions for non-linear fractional partial integro-differential equations (FPIDEs). The key novelty of the suggested method is that it can be used for handling solutions of non-linear FPIDEs in a very simple and effective way. {More precisely, we show that Daftardar--Jafari polynomials have simple calculations as compared to Adomian polynomials with higher accuracy}. The results obtained within the Daftardar--Jafari polynomials are demonstrated with graphs and tables, and the IATM's absolute error confirms the higher accuracy of the suggested method. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_11676 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Iterative Procedure for Non-Linear Fractional Integro-Differential Equations via Daftardar--Jafari Polynomials Khan, Qasim Suen, Anthony Numerical Analysis Analysis of PDEs In this paper, we introduce a novel approach called the Iterative Aboodh Transform Method (IATM) which utilizes Daftardar--Jafari polynomials for solving non-linear problems. Such method is employed to derive solutions for non-linear fractional partial integro-differential equations (FPIDEs). The key novelty of the suggested method is that it can be used for handling solutions of non-linear FPIDEs in a very simple and effective way. {More precisely, we show that Daftardar--Jafari polynomials have simple calculations as compared to Adomian polynomials with higher accuracy}. The results obtained within the Daftardar--Jafari polynomials are demonstrated with graphs and tables, and the IATM's absolute error confirms the higher accuracy of the suggested method. |
| title | Iterative Procedure for Non-Linear Fractional Integro-Differential Equations via Daftardar--Jafari Polynomials |
| topic | Numerical Analysis Analysis of PDEs |
| url | https://arxiv.org/abs/2502.11676 |