Optimal Conjugate Gradient with Spline Scheme for Solving Bagley-Torvik Fractional Differential Problems

Abstract

In this work, a non-polynomial spline function is constructed to solve the Bagley-Torvik Fractional Differential Problems
involving derivatives in the Caputo sense. This method transforms the fractional differential equation into a system of linear equations
using a spline scheme. The conjugate gradient method is employed for the iterative solution of the linear system. To validate the accuracy
of the method, numerical examples with known analytical solutions are tested. The numerical experiments demonstrate satisfactory
agreement with the exact solution.