ابوالفضل رشيدي

This thesis presents a novel approach for solving partial differential equations with fractional derivatives (FPDEs) through the application of artificial neural networks. Numerical solutions to FPDEs are obtained using a Hermite wavelet neural network (HWNN) framework. The Caputo fractional derivative is consistently employed to han‎dle fractional-order partial differential problems. To improve computational efficiency an‎d enhance input representation, the hidden layer is omitted from the model architecture. A feed-forward neural network with unsupervised error backpropagation is utilized to optimize network parameters an‎d minimize approximation errors. Numerical experiments validate the proposed method, demonstrating its effectiveness an‎d computational efficiency in accurately solving FPDEs.

معادلات ديفرانسيل جزئي كسري , مشتق كسري كاپوتو , چندجمله‌اي‌هاي موجك هرميت , شبكه عصبي , شبكه عصبي موجك

Fractional partial differential equations , Caputo fractional derivative , Hermite wavelet polynomials , Neural network , Wavelet neural network

Abolfazl Rashidi

Javad Vahidi