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Some Results on the q -Calculus and Fractional q -Differential Equations

Author

Listed:
  • Ying Sheng

    (Department of Mathematics, Northeastern University, Shenyang 110167, China
    These authors contributed equally to this work.)

  • Tie Zhang

    (Department of Mathematics, Northeastern University, Shenyang 110167, China
    These authors contributed equally to this work.)

Abstract

In this paper, we first discuss some important properties of fractional q -calculus. Then, based on these properties and the q -Laplace transform, we translate a class of fractional q -differential equations into the equivalent q -differential equations with integer order. Thus, we propose a method for solving some linear fractional q -differential equations by means of solving the corresponding integer order equations. Several examples are provided to illustrate our solution method.

Suggested Citation

  • Ying Sheng & Tie Zhang, 2021. "Some Results on the q -Calculus and Fractional q -Differential Equations," Mathematics, MDPI, vol. 10(1), pages 1-15, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2021:i:1:p:64-:d:711181
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