Mathematics الرياضيات

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Fractional Newton-Raphson Method
(Al-Quds University, 2025-04-13) Mohammad Imad Hammo; محمد عماد حمو
Fractional Calculus has found numerous applications across various scientific fields. In this thesis, we review key definitions of fractional derivatives and explore their applications. Specifically, we focus on three fractional derivative definitions and apply then to Newton-Raphson's method for solving equations. We implement these methods in python to compute polynomial roots and compare their performance in terms of iteration speed and accuracy. Our analysis highlights which definition yields faster convergence and better results. In this thesis, we enhance the Newton-Raphson method by replacing the ordinary derivative with the proposed fractional derivatives and apply this modified approach to solve various equations numerically and compare the results with the original Newton-Raphson method. Furthermore we conduct a comprehensive performance analysis to compare the numerical efficiency and accuracy of the modified methods.