Solving Linear and Nonlinear Duffing Fractional Differential Equations Using Cubic Hermite Spline Functions
Year: 2024
Type: article
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.
Authors: Mehrdad Lakestani, Roya Ghasemkhani
Institutions: University of Tabriz, University of Jiroft
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6926169830