A computationally efficient fractional predictor corrector approach involving the Mittag Leffler kernel
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908628393394176 |
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| author | Aljhani, Sami |
| author_facet | Aljhani, Sami |
| contents | In this paper, based on Newton interpolation we have proposed a numerical scheme of predictor-corrector type in order to solve fractional differential equations with the fractional derivative involving the Mittag-Leffler function. We have added an auxiliary midpoint in each sub-interval, this allows us to use a piecewise quadratic Newton interpolation to derive the corrector scheme. The derivation of the schemes for the midpoint and the predictor is done by means of a piecewise linear Newton interpolation. We present some illustrative examples for initial value problems that involve fractional derivatives in the sense of Atangana-Baleanu. The results of numerical experiments show that the proposed scheme is a powerful technique to handle fractional differential equations with nonlinear terms that involve operators of Atangana-Baleanu type. Moreover, the proposed method significantly improves the numerical accuracy in comparison with other methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_02822 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A computationally efficient fractional predictor corrector approach involving the Mittag Leffler kernel Aljhani, Sami Numerical Analysis In this paper, based on Newton interpolation we have proposed a numerical scheme of predictor-corrector type in order to solve fractional differential equations with the fractional derivative involving the Mittag-Leffler function. We have added an auxiliary midpoint in each sub-interval, this allows us to use a piecewise quadratic Newton interpolation to derive the corrector scheme. The derivation of the schemes for the midpoint and the predictor is done by means of a piecewise linear Newton interpolation. We present some illustrative examples for initial value problems that involve fractional derivatives in the sense of Atangana-Baleanu. The results of numerical experiments show that the proposed scheme is a powerful technique to handle fractional differential equations with nonlinear terms that involve operators of Atangana-Baleanu type. Moreover, the proposed method significantly improves the numerical accuracy in comparison with other methods. |
| title | A computationally efficient fractional predictor corrector approach involving the Mittag Leffler kernel |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2511.02822 |