(1)Numerical solution of fractional Mathieu equations by using block-pulse wavelets

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P. Pirmohabbati a,  A.H. Refahi Sheikhani ^a,∗, H. Saberi Najafi ^a,  A. Abdolahzadeh Ziabari ^b

^a Department of Applied Mathematics, Faculty of Mathematical Sciences, Lahijan Branch, Islamic Azad University, Lahijan, Iran 

^b Department of physics, Faculty of Science, Lahidjan Branch, Islamic Azad University, Lahidjan, Iran 

Received 25 February 2019; received in revised form 14 May 2019; accepted 15 May 2019 

Available online 21 May 2019 

Abstract

    In this paper, we introduce a method based on operational matrix of fractional order integration for the numerical solution of fractional Mathieu equation and then apply it in a number of cases. For this, we use the block-pulse wavelets matrix of fractional order integration with respect to the Caputo sense. The method was tested by some numerical examples and changes occurred in the coefficients as well as in the derivative of the equation. Results prove the accuracy and computational efficiency of the proposed algorithm. 

© 2019 Shanghai Jiaotong University. Published by Elsevier B.V. 

This is an open access article under the CC BY-NC-ND license. (http://creativecommons.org/licenses/by-nc-nd/4.0/)  

Keywords: Block-pulse functions; Fractional calculus; Mathieu differential equation.