Authors: Rajković, Predrag
Marinković, Slađana
Stanković, Miomir 
Title: Fractional integrals and derivatives in q-calculus
Journal: Applicable Analysis and Discrete Mathematics
Volume: 1
Issue: 1
First page: 311
Last page: 323
Issue Date: 1-Apr-2007
ISSN: 14528630
DOI: 10.2298/AADM0701311R
Abstract: 
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 | Fractional calculus | q-derivative | q-integral

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