Using operational matrix for numerical solution of fractional differential equations

In this article, we have discussed a new application of modification of hat functions on nonlinear multi-order fractional differential equations. The operational matrix of fractional integration is derived and used to transform the main equation to a system of algebraic equations. The method provides the solution in the form of a rapidly convergent series. Furthermore, error analysis of the proposed method is provided under several mild conditions. Three numerical examples are given to show the efficiency and accuracy of the method. Illustrative examples are included to demonstrate the validity, efficiency, and applicability of the method.