An Efficient Numerical Method for Solving a Class of Nonlinear Fractional Differential Equations and Error Estimates

Xin Song () and Rui Wu
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Xin Song: School of Data Science and Engineering, South China Normal University, Shanwei 516600, China
Rui Wu: School of Mathematics and Statistics, Changchun University of Technology, Changchun 130012, China

Mathematics, 2024, vol. 12, issue 12, 1-12

Abstract: In this paper, we present an efficient method for solving a class of higher order fractional differential equations with general boundary conditions. The convergence of the numerical method is proved and an error estimate is given. Finally, eight numerical examples, both linear and nonlinear, are presented to demonstrate the accuracy of our method. The proposed method introduces suitable base functions to calculate the approximate solutions and only requires us to deal with the linear or nonlinear systems. Thus, our method is convenient to implement. Furthermore, the numerical results show that the proposed method performs better compared to the existing ones.

Keywords: fractional differential equations; approximate solutions; base functions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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