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New spectral techniques for systems of fractional differential equations using fractional-order generalized laguerre orthogonal functions

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2014

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Walter De Gruyter GMBH

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Abstract

Fractional-order generalized Laguerre functions (FGLFs) are proposed depends on the definition of generalized Laguerre polynomials. In addition, we derive a new formula expressing explicitly any Caputo fractional-order derivatives of FGLFs in terms of FGLFs themselves. We also propose a fractional-order generalized Laguerre tau technique in conjunction with the derived fractional-order derivative formula of FGLFs for solving Caputo type fractional differential equations (FDEs) of order nu (0 < nu < 1). The fractional-order generalized Laguerre pseudo-spectral approximation is investigated for solving nonlinear initial value problem of fractional order nu. The extension of the fractional-order generalized Laguerre pseudo-spectral method is given to solve systems of FDEs. We present the advantages of using the spectral schemes based on FGLFs and compare them with other methods. Several numerical example are implemented for FDEs and systems of FDEs including linear and nonlinear terms. We demonstrate the high accuracy and the efficiency of the proposed techniques.

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Multi-Term Fractional Differential Equations, Fractional-Order Generalized Laguerre Orthogonal Functions, Generalized Laguerre Polynomials, Tau Method, Pseudo-Spectral Methods

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Citation

Bhrawy, AH...et.al. (2014). "New spectral techniques for systems of fractional differential equations using fractional-order generalized laguerre orthogonal functions" Fractional Calculus and Applied Analysis, Vol.17, No.4, pp.1137-1157.

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Fractional Calculus and Applied Analysis

Volume

17

Issue

4

Start Page

1137

End Page

1157