Collocation Method for the Numerical Solution of Multi-Order Fractional Differential Equations

Abstract

This study presents a collocation approach for the numerical integration of multi-order fractional differential equations with initial conditions in the Caputo sense. The problem was transformed from its integral form into a system of linear algebraic equations. Using matrix inversion, the algebraic equations are solved and their solutions are substituted into the approximate equation to give the numerical results. The effectiveness and precision of the method were illustrated with the use of numerical examples.