Relations Between the Fractional Operators in q-Calculus
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In this survey paper, we will consider the fractional operators in q-calculus. Starting from the fractional versions of q-Pochhammer symbol, we generalize the notions of the fractional q-integral and q-derivative by introducing variable lower bound of integration. We discuss their properties, describe relations which connect them, and illustrate notions and results with examples and counterexamples.
KeywordsFractional q-integral Fractional q-derivative
MSC 2010 Classification05A30 26A33 33D05
This research was financially supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia. The second author is grateful to Mathematics and Applied Mathematics Research Environment at the School of Education, Culture and Communication at Mälardalen University for cordial hospitality and cooperation during his research stay.
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