On Some Fractional Pearson Equations

Fractional Calculus and Applied Analysis

Volumn 18, Issue 5, 2015, Pages 1164-1178

  Area, Ivan ^a   Losada, Jorge ^b   Manintchap, Ariane ^c  

^a UNIVERSITY OF VIGO   (Spain)

^b UNIVERSITY OF SANTIAGO DE COMPOSTELA   (Spain)

^c African Institute for Mathematical Sciences (AIMS) Limbe Crystal Gardens   (Cameroon)

Author keywords

fractional calculus; fractional Pearson equation; quasi orthogonal polynomials

Indexed keywords

EID: 84937805650     PISSN: 13110454     EISSN: 13142444     Source Type: Journal    
DOI: 10.1515/fca-2015-0067     Document Type: Article

References (19)

1. T.S. Chihara, An Introduction to Orthogonal Polynomials. Gordon and Breach Science Publishers, New York (1978).
2. R.A. Horn and C.R. Johnson, Matrix Analysis. 2nd Ed., Cambridge University Press, Cambridge (2013).
3. M.E.H. Ismail, Classical and Quantum Orthogonal Polynomials in One Variable. Cambridge University Press, Cambridge (2005).
4. N.L. Johnson, S. Kotz, and N. Balakrishnan, Continuous Univariate Distributions. 2nd Ed., John Wiley & Sons Inc. (1994).
5. A.A. Kilbas, H.M. Srivastava, and J.J. Trujillo, Theory and Applications of Fractional Differential Equations. Elsevier Science B.V., Amsterdam (2006).
6. V. Kiryakova, Generalized Fractional Calculus and Applications. Longman Scientific & Technical, Harlow; copubl. by John Wiley & Sons, Inc., New York (1994).
7. R. Koekoek, P.A. Lesky, and R.F. Swarttouw, Hypergeometric Orthogonal Polynomials and their q-Analogues. Springer-Verlag, Berlin (2010).
8. C. Li, F. Zeng, and F. Liu, Spectral approximations to the fractional integral and derivative. Fract. Calc. Appl. Anal. 15, No 3 (2012), 383-406; DOI: 10.2478/s13540-012-0028-x; http://www.degruyter.com/view/j/fca.2012.15.issue-3/ issue-files/fca.2012.15.issue-3.xml.
9. A.F. Nikiforov, S.K. Suslov, and V.B. Uvarov, Classical Orthogonal Polynomials of a Discrete Variable. Springer-Verlag, Berlin (1991).
10. P. Njionou Sadjang, W. Koepf, and M. Foupouagnigni, On moments of classical orthogonal polynomials. J. Math. Anal. Appl. 424 (2015), 122-151.
11. K. Pearson, Contributions to the mathematical theory of evolution, II. Skew variation in homogeneous material. Royal Soc. of London Phil. Transactions Ser. A 186 (1895), 343-414.
12. I. Podlubny, Fractional Differential Equations. Academic Press, Inc., San Diego, CA (1999).
13. M.R. Rapaić, T.B. Sekara, and V. Govedarica, A novel class of fractionally orthogonal quasi-polynomials and new fractional quadrature formulas. Appl. Math. Comput. 245 (2014), 206-219.
14. S.G. Samko, A.A. Kilbas, and O.I. Marichev, Fractional Integrals and Derivatives. Taylor & Francis (1993).
15. P.J. Szabłowski, A few remarks on orthogonal polynomials. Appl. Math. Comput. 252 (2015), 215-228.
16. G. Szego, Orthogonal Polynomials. 4th Ed., American Mathematical Society, Providence, R.I. (1975).
17. J. Tenreiro Machado, A. Lopes, F. Duarte, M. Ortigueira, R. Rato, Rhapsody in fractional. Fract. Calc. Appl. Anal. 17, No 4 (2014), 1188-1214; DOI: 10.2478/s13540-014-0206-0; http://www.degruyter.com/view/j/fca.2014.17.issue-4/ issue-files/fca.2014.17.issue-4.xml.
18. J. Tenreiro Machado, F. Mainardi, V. Kiryakova, Fractional calculus: Quo Vadimus? (Where are we going?). Fract. Calc. Appl. Anal. 18, No 2 (2015), 495-526; DOI: 10.1515/fca-2015-0031; http://www.degruyter.com/view/j/fca.2015.18.issue-2/ issue-files/fca.2015.18.issue-2.xml.
19. Wolfram Research, Inc., Mathematica, Version 10.1.0.0. Champaign, Illinois (2015).