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Legendre-collocation spectral solver for variable-order fractional functional differential equations | ||
| Computational Methods for Differential Equations | ||
| مقاله 7، دوره 8، شماره 1، فروردین 2020، صفحه 99-110 اصل مقاله (411 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2019.9465 | ||
| نویسندگان | ||
| Ramy Mahmoud Hafez1؛ Youssri Hassan Youssri* 2 | ||
| 1Department of Mathematics, Faculty of Education, Matrouh University, Egypt. | ||
| 2Department of Mathematics, Faculty of Science, Cairo University, Giza-Egypt | ||
| چکیده | ||
| A numerical method for the variable-order fractional functional differential equations (VO-FFDEs) has been developed. This method is based on approximation with shifted Legendre polynomials. The properties of the latter were stated, first. These properties, together with the shifted Gauss-Legendre nodes were then utilized to reduce the VO-FFDEs into a solution of matrix equation. Sequentially, the error estimation of the proposed method was investigated. The validity and efficiency of our method were examined and verified via numerical examples. | ||
| کلیدواژهها | ||
| Variable-order fractional functional differential equations؛ Shifted Legendre polynomials؛ Gauss-Legendre nodes؛ Matrix equation | ||
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