Haar wavelet operational matrix of fractional order integration and its applications in solving the fractional order differential equations. (English) Zbl 1193.65114

Summary: Haar wavelet operational matrix has been widely applied in system analysis, system identification, optimal control and numerical solution of integral and differential equations. In the present paper we derive the Haar wavelet operational matrix of the fractional order integration, and use it to solve the fractional order differential equations including the Bagley-Torvik, Riccati and composite fractional oscillation equations. The results obtained are in good agreement with the existing ones in open literatures and it is shown that the technique introduced here is robust and easy to apply.


65L05 Numerical methods for initial value problems involving ordinary differential equations
34A08 Fractional ordinary differential equations
65T60 Numerical methods for wavelets
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