IJPAM: Volume 105, No. 1 (2015)

LEGENDRE WAVELET OPERATIONAL MATRIX
OF FRACTIONAL DERIVATIVE
THROUGH WAVELET-POLYNOMIAL TRANSFORMATION
AND ITS APPLICATIONS IN SOLVING FRACTIONAL ORDER
DIFFERENTIAL EQUATIONS

Abdulnasir Isah$^1$, Pang Chang$^2$
$^{1,2}$Department of Mathematics and Statistics
University Tun Hussein Onn Malaysia
86400, Batu Pahat, Johor, MALAYSIA


Abstract. In this paper we present a numerical method for solving fractional differential equations(FDEs) based on Legendre wavelets. The known Legendre Wavelets is presented first then we derived the operational matrix of fractional order derivative through wavelet-polynomial transformation matrix which was utilised together with spectral and collocation methods to reduce the linear and non-linear FDEs to a system of algebraic equations respectively. The method presented represents a more simple technique of obtaining the operational matrix with straight forward applicability to the FDEs in comparison to the existing operational matrices, most of which obtained either by direct integration of the wavelet vector or through block pulse functions. Results obtained when solving different linear and non-linear FDEs confirm the applicability and accuracy of the proposed method.

Received: August 7, 2015

AMS Subject Classification: 34K37, 42C40, 65T60

Key Words and Phrases: shifted Legendre polynomials, Legendre wavelets, operational matrix, fractional derivatives

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DOI: 10.12732/ijpam.v105i1.9 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 105
Issue: 1
Pages: 97 - 114


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