Authors: Stanković, Miomir 
Rajković, Predrag
Marinković, Slađana
Title: On fractional q-integrals, q-derivatives and corresponding equations
Journal: AIP Conference Proceedings
Volume: 1186
First page: 300
Last page: 308
Issue Date: 22-Dec-2009
ISSN: 0094-243X
DOI: 10.1063/1.3265343
Based on the fractional q-integral with the parametric lower limit of integration, we define fractional q-derivative of Riemann-Liouville and Caputo type. The properties are studied separately as well as relations between them and their compositions. Also, we consider usage of Picard-Lindelöf method for the solving the corresponding differential equations.
Keywords: Basic hypergeometric functions | Caputo derivative | Fractional calculus | Riemann-Liouville derivative
Publisher: American Institute of Physics

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