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Numerical Solution of Nonlinear Fractional Delay Differential Equations Using Fractional Jacobi Functions and Picard Iteration | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 19 تیر 1405 اصل مقاله (1.39 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2026.67629.3230 | ||
| نویسندگان | ||
| Soheyla Ansari؛ Mohammad Hossein Akrami* | ||
| Department of Mathematical Sciences, Yazd University, Yazd, Iran. | ||
| چکیده | ||
| This paper presents a novel numerical method for solving nonlinear fractional delay differential equations. Our approach uses fractional Jacobi functions in conjunction with a straightforward Picard iteration scheme to construct numerical solutions. Unlike some existing techniques, the proposed method is computationally efficient and avoids complex calculations. The use of orthogonal functions within the Picard iterations provides accurate approximations. Also, a convergence analysis demonstrates the method's high accuracy. We demonstrate the method's applicability and effectiveness by solving several challenging fractional delay differential equations, including the fractional pantograph equation and the fractional Hutchinson model. The results confirm that our method performs better than other numerical methods. | ||
| کلیدواژهها | ||
| Fractional Jacobi functions؛ Picard iterations method؛ Fractional pantograph equation؛ Fractional Hutchinson model | ||
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آمار تعداد مشاهده مقاله: 63 تعداد دریافت فایل اصل مقاله: 71 |
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