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.
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Njionou Sadjang, P., Mboutngam, S. A fractional q-derivative operator and fractional extensions of some q-orthogonal polynomials. Ramanujan J 54, 29–41 (2021). https://doi.org/10.1007/s11139-019-00181-w
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DOI: https://doi.org/10.1007/s11139-019-00181-w
Keywords
- q-Fractional calculus
- Fractional q-derivative
- q-Hypergeometric functions
- q-Orthogonal polynomials
- Fractional q-differential equations