A fractional q-derivative operator and fractional extensions of some q-orthogonal polynomials
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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 equationsMathematics Subject Classification
26A33 33D15 39A13 39A70Notes
References
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