Numerical solution to fractional Cauchy problem

Abstract

This thesis investigates the numerical solutions to fractional Cauchy problems utilizing the Finite Difference Method. The work focuses on the formulation and simulation of fractional differential equations governed by the Caputo fractional derivative. An integrated discrete numerical scheme is constructed, and its stability properties along with convergence analyses are established. Finally, illustrative numerical experiments are performed and compared against exact analytical trajectories to validate the proposed method.