Other Mathematics Commons^™

Fractals, Fractional Derivatives, And Newton-Like Methods, Eleanor Byrnes

HMC Senior Theses

Inspired by the fractals generated by the discretizations of the Continuous Newton Method and the notion of a fractional derivative, we ask what it would mean if such a fractional derivative were to replace the derivatives in Newton's Method. This work, largely experimental in nature, examines these new iterative methods by generating their Julia sets, computing their fractal dimension, and in certain tractable cases examining the behaviors using tools from dynamical systems.