Open AccessNumerical Study of Fractional Mathieu Differential Equation Using Radial Basis Functions
Author(s) -
Hojjat Ghorbani,
Yaghoub Mahmoudi,
Farhad Dastmalchi Saei
Publication year - 2020
Publication title -
mathematical modelling and engineering problems/mathematical modelling of engineering problems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.26
H-Index - 11
eISSN - 2369-0747
pISSN - 2369-0739
DOI - 10.18280/mmep.070409
Subject(s) - mathieu function , mathematics , singularity , mathematical analysis , radial basis function , differential equation , numerical integration , fractional calculus , basis (linear algebra) , numerical analysis , integro differential equation , first order partial differential equation , geometry , computer science , machine learning , artificial neural network
In this paper, we introduce a method based on Radial Basis Functions (RBFs) for the numerical approximation of Mathieu differential equation with two fractional derivatives in the Caputo sense. For this, we suggest a numerical integration method for approximating the improper integrals with a singularity point at the right end of the integration domain, which appear in the fractional computations. We study numerically the affects of characteristic parameters and damping factor on the behavior of solution for fractional Mathieu differential equation. Some examples are presented to illustrate applicability and accuracy of the proposed method. The fractional derivatives order and the parameters of the Mathieu equation are changed to study the convergency of the numerical solutions.