” Numerical Solution of Fractional Neutral Functional-Differential Equations by the Operational Tau Method ”
S. Kouhkani , H. Koppelaar , M. Abri … 2017 , No.1 , P. 5 – 19
We develop an extension of the algebraic formulation of the Operational Tau Method (OTM) based upon shifted Chebyshev polynomials. This extension enables us to improve numerical precision of solving Fractional Neutral Functional-Differential equations (FNFDEs) from Bhrawy and Algamdi  as we show in this paper.
1. C. Lanczos. Trigonometric interpolation of empirical and analytic functions. J. Math. Physics, Vol. 17, 1938,123-199.
2. E.L. Ortiz, H. Samara. An operational approach to the tau method for the numerical solution of non-linear differential equations. Computing, Vol. 27, 1981, pp. 15-25.
3. K. M. Liu, C. K. Pan. The automatic solution to systems of ordinary differential equations by the tau method. Computer and Mathematics with Applications,Vol. 38, 1999, pp. 197-210.
4. J. SedigiHafshejani, S. KarimiVanani, J.Esmaily. Operational tau approximation for neutral delay differential systems. Journal of Applied Science, 14, 2011, pp. 2585-2591.
5. K. B. Oldham, J.Spainer. The Fractional Calculus. Academic Press, New York/London, 1974.
6. I. Podlubny. Fractional differential equations. Academic Press, New York, 1999.
7. A.A. Kilbas, H.M. Srivastava, J.J. Trujillo. Theory and applications of fractional differential equations. North-holland Mathematics Studies. Elsevier, Amsterdam, 2006.
8. A.H. Bhrawy, M. A. Alghamdi. A shifted Jacobi Gauss collocation scheme for solving fractional neutral functional-differential equations. Advances in Mathematical Physics, Vol. 2014, 2014, pp. 1 – 8.
9. AytacArikoglu, Ibrahim Ozkol. Solution of fractional differential equations by using differential transform method. Chaos Solution & Fractals,Vol. 34, 2007, pp. 1473-1481.
10. S. KarimiVanani, A. Aminataei. Operational tau approximation for a general class of fractional integro-differential equations. Computational and Applied Mathematics,Vol. 30, 2011, pp. 655-674.
11. F. Ghoreishi, S. Yazdani. An extension of the spectral tau method for numerical solution of multi- order fractional equations with convergence analysis. Computers and Mathematics with Applications, Vol. 61, 2011, pp. 30-43.
12. A.H. Bhrawy, A.S. Alofi, S.S. Ezz-Eldien. A quadrature tau method for fractional differential equations with variable coefficients. Applied Mathematics Letters, Vol. 24, 2011, pp. 2146-2152.
13. M.Y. Rahimi-Ardabili, S. Shahmorad. Iterative numerical solution of non-linear integro-differential equations by the Tau method. Applied Mathematics and Computation, Vol. 193, 2007, pp. 514-522.