Solving Linear and Nonlinear Fractional Differential Equations Using Spline Functions

Abstract

Suitable spline functions of polynomial form are derived and used to solve linear and nonlinearfractional differential equations. The proposed method is applicable for and $\alpha \ge 1$, where $\alpha$ denotes the order of the fractional derivative in the Caputo sense. The results obtainedare in good agreement with the exact analytical solutions and the numerical results presentedelsewhere. Results also show that the technique introduced here is robust and easy to apply.