Numerical solution of Fractional Neutral Functional Differential Equations by A shifted Chebyshev computational matrix

” Numerical solution of Fractional Neutral Functional Differential Equations by A shifted Chebyshev computational matrix ” , S.Kouhkani , H. Koppelaar …2018, No.1 , P. 5 – 14 

DOI :   http://dx.doi.org/10.22039/cjcme.2018.07

Abstract :

In this article, we develop a direct solution technique for solving Fractional Neutral Functional-Differential Equations (FNFDEs) using a matrix method based upon the shifted Chebyshev tau and shifted Chebyshev collocation method. The fractional derivatives are described in the Caputo sense. The main characteristic behind the approach using this technique is that it reduces the problems to a system of algebraic equations. The results reveal that the proposed method is very effective and simple.

REFERENCES : 

1. K. B. Oldham, J. Spainer. The fractional calculus, first ed., Academic Press, New York/       London,1974.

2. I. Podlubny. Fractional differential equations, first ed., Academic Press. New York,1999.

3. A. A. Kilbas, H. M. Sirvasta, J. J. Trujillo. Theory and applications of fractional                differential equations, first ed., North- Holland Mathematics studies. Elsevier. Amsterdom, 2006.

4. D. Gottlieb, S. A. Orszag. Numerical analysis of spectral methods: Theory and Applications, first ed., Society for Industrial and Applied Mathematics, 1977.

5. A. Saadatmandi, M. Dehghan. A new operational matrix for solving fractional- order differential equations, Computers and Mathematics with Applications, N.59, 2010, pp.1326-1336.

6. A. H. Bhrawy, A. Alghamdi. A shifted Jacobi Guass collocation scheme for solving fractional neutral functional- differential equations, Advances in Mathematics Physics. N.2014, 2014, pp.1-8.

7. A. H. Bhrawy, A. S. Alofi. The operational matrix of fractional integration for shifted Chebyshev polynomials, Applied Mathematics Letters. N.26, 2013, pp.25-31.

8. E. H. Doha, A. H. Bhrawy, S. S. Ezz- Eldien. Efficient Chebyshev spectral methods for solving multi-term fractional order differential equations, Applied Mathematics Modelling. N.35, 2011, pp.5662-5672.

9. N. H. Sweilam, M. M. Khader, W. Y. Kota. Numerical and analytical study for fourth- order integro- differential equations using a pseudospectral method, Mathematical problems in engineering. N.2013, 2013.

10. M. M. Khader, A. S. Hendy. The approximate and exact solution of the fractional- order delay differential equations using Legendre seudospectral method, International Journal of Pure and Applied Mathematics, .N.74, 2012, pp.287-297.

11. A. H. Bhrawy, M. A. Zaky, J. A. Tenreiro Machado. Numerical solution of the two- sided space- time fractional telegraph equation via Chebyshev tau approximation, J. Optim Theory, 2016, pp.1-22.

12. S. Kouhkani, H. Koppelaar, M. Abri. Numerical solution of fractional neutral functional- differential equations by the operational tau method, CJCME. 2017 No.1, 2017, pp.5-19.

13. H. Khalil, R. A. Khan, M. H. AL- Samdi, A. A. Freihat, N. Shawagfeh. New operational matrix for shifted Legendre polynomials and fractional differential equations with variable coefficients, Journal of Mathematics (Punjab University), Vol. 47, 2.15, pp.1-24.