Solving‎ ‎Linear and‎ ‎Nonlinear Duffing‎ ‎Fractional Differential Equations Using Cubic Hermite Spline Functions

Abstract

‎In this work‎, ‎we solve nonlinear Duffing fractional differential equations with integral boundary conditions in the Caputo fractional order derivative sense‎. ‎First‎, ‎we introduce the cubic Hermite spline functions and give some properties of these functions‎. ‎Then we make an operational matrix to the fractional derivative in the Caputo sense‎. Using this matrix and derivative matrices of integers (first and second order) and applying collocation method‎, ‎we convert nonlinear Duffing equations into a system of algebraic equations that can be solved to find the approximate solution‎. Numerical examples show the applicability and efficiency of the suggested method‎. ‎Also‎, ‎we give a numerical convergence order for the presented method in this part‎.

Keywords

• duffing fractional differential equations‎
• ‎cubic hermite spline functions‎
• ‎caputo derivative‎
• ‎operational matrix