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

Document Type : Original Scientific Paper

Authors

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

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.

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Main Subjects

References

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Mathematics Interdisciplinary Research
Volume 9, Issue 4
December 2024
Pages 425-442

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