A fractional q-derivative operator and fractional extensions of some q-orthogonal polynomials

  • P. Njionou SadjangEmail author
  • S. Mboutngam


A fractional q-derivative operator is introduced and some of its properties have been proved. Next, a fractional q-differential equation of Gauss type is introduced and solved by means of a power series method. Finally, q-extensions of some classical q-orthogonal polynomials are introduced and some of the main properties of the newly defined functions are given.


q-Fractional calculus Fractional q-derivative q-Hypergeometric functions q-Orthogonal polynomials Fractional q-differential equations 

Mathematics Subject Classification

26A33 33D15 39A13 39A70 



  1. 1.
    Annaby, M.H., Mansour, Z.S.: \(q\)-Fractional Calculus and Equations. Springer, New York (2012)Google Scholar
  2. 2.
    Fischer, K.K.: Identifikation Spezieller Funktionen, Die Durch Rodriguesformeln Gegeben Sind, PhD thesis, Universität Kassel (2016).
  3. 3.
    Gasper, G., Rahman, M.: Basic Hypergeometric Series. Encyclopedia of Mathematics and its Applications, vol. 35. Cambridge University Press, Cambridge (1990)zbMATHGoogle Scholar
  4. 4.
    Koekoek, R., Lesky, P.A.: Swarttouw RF Hypergeometric Orthogonal Polynomials and Their \(q\)-Analogues. Springer, New York (2010)Google Scholar
  5. 5.
    Koorwinder, T.H.: \(q\)-Special Functions, a Tutorial (2013).
  6. 6.
    Rainville, E.D.: Special Functions. The Macmillan Company, New York (1960)zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Faculty of Industrial EngineeringUniversity of DoualaDoualaCameroon
  2. 2.Higher Teachers’ Training CollegeUniversity of MarouaMarouaCameroon

Personalised recommendations