Solving Linear and Nonlinear Duffing Fractional Differential Equations Using Cubic Hermite Spline Functions
نویسندگان
1 Department of Applied Mathematics, Faculty of Mathematics, Statistics and Computer Science, University of Tabriz, Tabriz, I. R. Iran
2 Department of Mathematics, Faculty of Science, University of Jiroft, Jiroft, I. R. Iran
doi
10.22052/mir.2024.254944.1463چکیده
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.
