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Solving Fractional Differential Equations involving YAC Operator using ANN | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 12 بهمن 1404 اصل مقاله (1.71 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2025.66444.3102 | ||
| نویسندگان | ||
| Manoj Kumar* 1؛ Pranay Goswami2 | ||
| 1School of Sciences, IILM University, Greater Noida, India. | ||
| 2School of Liberal Studies, Ambedkar University Delhi, New Delhi, India. | ||
| چکیده | ||
| Most real-world phenomena, particularly in biological systems, are modeled using differential equations. However, certain classes of differential equations, especially nonlinear fractional differential equations (FDEs), pose significant analytical challenges. In this paper, we propose a novel Artificial Neural Network (ANN) framework for solving nonlinear FDEs based on the Yang-Abdel-Cattani (YAC) fractional derivative operator. The proposed method employs a truncated power series expansion as a trial solution, with unknown coefficients determined through an iterative optimization process guided by the ANN architecture. By integrating neural networks with fractional-order modeling, the proposed approach offers an efficient and accurate solution strategy for complex FDEs. Numerical results demonstrate that the method achieves higher accuracy and reliability compared to existing works [2]. | ||
| کلیدواژهها | ||
| Fractional Differential Equations؛ Approximate Numerical Solutions؛ Neural Networks for Approximation؛ Unsupervised Machine Learning | ||
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آمار تعداد مشاهده مقاله: 89 تعداد دریافت فایل اصل مقاله: 117 |
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