Abstract
In this paper, we derived a new operational matrix of fractional integration of arbitrary order for modified generalized Laguerre polynomials. The fractional integration is described in the Riemann-Liouville sense. This operational matrix is applied together with the modified generalized Laguerre tau method for solving general linear multi-term fractional differential equations (FDEs). Only small dimension of a modified generalized Laguerre operational matrix is needed to obtain a satisfactory result. Illustrative examples reveal that the present method is very effective and convenient for linear multi-term FDEs on a semi-infinite interval.
Highlights
Fractional differential equations have drawn the interest of many researchers due to their important applications in science and engineering
We propose a new tau method based on the operational matrix of fractional integration in the Riemann-Liouville sense, in which we take the modified Laguerre functions as the basis functions and approximate the solutions of multi-term fractional differential equations (FDEs) on a semi-infinite interval
6 Conclusion In this paper, we introduced a general formulation for the modified generalized Laguerre operational matrix of fractional integration
Summary
Fractional differential equations have drawn the interest of many researchers (see, for instance, [ – ]) due to their important applications in science and engineering. It is interesting to consider spectral tau methods for solving multi-term FDEs on the half line by using the operational matrix of fractional integration of modified Laguerre polynomials. In [ ], Doha et al derived the Jacobi operational matrix of fractional derivatives which was applied together with the spectral tau method for a numerical solution of general linear multi-term fractional differential equations. Bhrawy and Alofi [ ] proposed the operational Chebyshev matrix of fractional integration in the Riemann-Liouville sense which was applied together with the spectral tau method to solve linear FDEs on a finite interval. We propose a new tau method based on the operational matrix of fractional integration in the Riemann-Liouville sense, in which we take the modified Laguerre functions as the basis functions and approximate the solutions of multi-term FDEs on a semi-infinite interval.
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