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Relations Between the Fractional Operators in q-Calculus

  • Sergei Silvestrov
  • Predrag M. RajkovićEmail author
  • Sladjana D. Marinković
  • Miomir S. Stanković
Conference paper
  • 39 Downloads
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 317)

Abstract

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.

Keywords

Fractional q-integral Fractional q-derivative 

MSC 2010 Classification

05A30 26A33 33D05 

Notes

Acknowledgements

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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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Sergei Silvestrov
    • 1
  • Predrag M. Rajković
    • 2
    Email author
  • Sladjana D. Marinković
    • 3
  • Miomir S. Stanković
    • 4
  1. 1.Division of Applied Mathematics, School of Education, Culture and CommunicationMälardalen UniversityVästeråsSweden
  2. 2.Faculty of Mechanical Engineering, Department of MathematicsUniversity of NišNišSerbia
  3. 3.Faculty of Electronic Engineering, Department of MathematicsUniversity of NišNišSerbia
  4. 4.Faculty of Occupation Safety, Department of MathematicsUniversity of NišNišSerbia

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