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