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Fractional integrals and derivatives in q-calculus

Rajković Predrag M. (Faculty of Mechanical Engineering, Department of Mathematics, Niš)
Marinković Slađana D. (Faculty of Electronic Engineering, Department of Mathematics, Niš)
Stanković Miomir S. (Faculty of Occupational Safety, Department of Mathematics)

We generalize the notions of the fractional q-integral and q-derivative by introducing variable lower limit of integration. We discuss some properties and their relations. Finally, we give a q-Taylor-like formula which includes fractional q-derivatives of the function.

Keywords: basic hypergeometric functions, q-integral, q-derivative, fractional calculus