Iterative methods for solving fractional differential equations using non-polynomial splines

In this work, a non-polynomial spline function is proposed to solve a linear fractional differential equation where the derivatives are in the Caputo sense. This approach transforms the fractional differential equation into a system of linear equations. The Gauss-Seidel and conjugate gradient methods are used to iteratively solve the linear system. Finally, to validate the method’s accuracy, several numerical examples with known analytical solutions are tested. According to the numerical experiments, the findings are in satisfactory agreement with the exact solutions.