The operational matrix of fractional integration for shifted Chebyshev polynomials

Applied Mathematics Letters

Volumn 26, Issue 1, 2013, Pages 25-31

  Bhrawy, A H ^a,b   Alofi, A S ^b  

^a Beni Suef University   (Egypt)

^b KING ABDULAZIZ UNIVERSITY   (Saudi Arabia)

Author keywords

Multi term FDEs; Operational matrix; Riemann Liouville derivative; Shifted Chebyshev polynomials; Tau method

Indexed keywords

ARBITRARY ORDER; CHEBYSHEV; FRACTIONAL INTEGRATION; ILLUSTRATIVE EXAMPLES; LINEAR FRACTIONAL DIFFERENTIAL EQUATIONS; MULTI-TERM FDES; NUMERICAL APPROACHES; OPERATIONAL MATRICES; RIEMANN-LIOUVILLE SENSE; SHIFTED CHEBYSHEV POLYNOMIALS; TAU METHOD;

INTEGRATION; MATRIX ALGEBRA; NUMERICAL METHODS;

POLYNOMIALS;

EID: 84866046515     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aml.2012.01.027     Document Type: Article

References (20)

1. S. Das Functional Fractional Calculus for System Identification and Controls 2008 Springer New York
2. A.A. Kilbas, H.M. Srivastava, and J.J. Trujillo Theory and Applications of Fractional Differential Equations 2006 Elsevier San Diego
3. I. Podlubny Fractional Differential Equations Mathematics in Science and Engineering vol. 198 1999 Academic Press Inc. San Diego, CA
4. C. Canuto, M.Y. Hussaini, A. Quarteroni, and T.A. Zang Spectral Methods in Fluid Dynamics 1988 Springer New York
5. E.H. Doha, and A.H. Bhrawy Efficient spectral-Galerkin algorithms for direct solution of fourth-order differential equations using Jacobi polynomials Appl. Numer. Math. 58 2008 1224 1244
6. E.H. Doha, A.H. Bhrawy, and M.A. Saker Integrals of Bernstein polynomials: an application for the solution of high even-order differential equations Appl. Math. Lett. 24 2011 559 565
7. Mujeeb ur Rehman, and Rahmat Ali Khan The Legendre wavelet method for solving fractional differential equations Commun. Nonlinear Sci. Numer. Simul. 16 2011 4163 4173
8. E.H. Doha, A.H. Bhrawy, and S.S. Ezz-Eldien Efficient Chebyshev spectral methods for solving multi-term fractional orders differential equations Appl. Math. Modell. 35 2011 5662 5672
9. S. Esmaeili, and M. Shamsi A pseudo-spectral scheme for the approximate solution of a family of fractional differential equations Commun. Nonlinear Sci. Numer. Simul. 16 2011 3646 3654
10. A. Saadatmandi, and M. Dehghan A new operational matrix for solving fractional-order differential equations Comput. Math. Appl. 59 2010 1326 1336
11. A.H. Bhrawy, A.S. Alofi, and S.S. Ezz-Eldien A quadrature tau method for fractional differential equations with variable coefficients Appl. Math. Lett. 24 2011 2146 2152
12. E.H. Doha, A.H. Bhrawy, and S.S. Ezz-Eldien A Chebyshev spectral method based on operational matrix for initial and boundary value problems of fractional order Comput. Math. Appl. 62 2011 2364 2373
13. C. Hwang, and Y.P. Shih Parameter identification via Laguerre polynomials Internat. J. Systems Sci. 13 1982 209 217
14. P.N. Paraskevopoulos Chebyshev series approach to system identification, analysis and control J. Franklin Inst. 316 1983 135 157
15. P.N. Paraskevopoulos Legendre series approach to identification and analysis of linear systems IEEE Trans. Automat. Control 30 6 1985 585 589
16. P.N. Paraskevopoulos, P. Sklavounos, and G.Ch. Georgiou The operational matrix of integration for Bessel functions J. Franklin Inst. 327 1990 329 341
17. A.K. Singh, V.K. Singh, and O.P. Singh The Bernstein operational matrix of integration Appl. Math. Sci. 3 49 2009 2427 2436
18. K. Maleknejad, B. Basirat, and E. Hashemizadeh Bernstein operational matrix approach for system of high order linear Volterra-Fredholm integro-differential equations Math. Comp. Model. 55 2012 1363 1372
19. K. Miller, and B. Ross An Introduction to the Fractional Calaulus and Fractional Differential Equations 1993 John Wiley & Sons Inc. New York
20. K. Diethelm, and N.J. Ford Multi-order fractional differential equations and their numerical solutions Appl. Math. Comput. 154 2004 621 640