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

  • P. Njionou SadjangEmail author
  • S. Mboutngam
Article
  • 14 Downloads

Abstract

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.

Keywords

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

Mathematics Subject Classification

26A33 33D15 39A13 39A70 

Notes

References

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    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

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