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

Ying Sheng and Tie Zhang
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Ying Sheng: Department of Mathematics, Northeastern University, Shenyang 110167, China
Tie Zhang: Department of Mathematics, Northeastern University, Shenyang 110167, China

Mathematics, 2021, vol. 10, issue 1, 1-15

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.

Keywords: fractional q -calculus; the fractional q -differential equations; equivalency theorem; solution method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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