Convergence Analysis of Numerical Methods for Fractional Differential and Integro-Differential Equations

Abstract

This thesis mainly focuses on the numerical solutions for the various types of fractional order differential and integrodifferential equations. We have discussed the ordinary, partial, and integro-partial differential equations involving RLC-type and Caputo-type fractional derivatives. The numerical methods we have proposed in this thesis are mainly the shooting method, the cubic spline, and the discontinuous Galerkin finite element method. Besides finding the numerical solutions, we have discussed the well-posedness of some of the problems.