Fractional q -symmetric calculus on a time scale

Advances in Difference Equations

Chengmin Hou¹  Mingzhe Sun¹ 

[1] Department of Mathematics, Yanbian University, Yanji, P.R. China

关键词: fractional q-symmetric exponential function;    fractional q-symmetric gamma function;    Laplace transform;    initial value problem;    92B20;    68T05;    39A11;    34K13;   

DOI  :  10.1186/s13662-017-1219-x

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, the definitions of q-symmetric exponential function and q-symmetric gamma function are presented. By a q-symmetric exponential function, we shall illustrate the Laplace transform method and define and solve several families of linear fractional q-symmetric difference equations with constant coefficients. We also introduce a q-symmetric analogue Mittag-Leffler function and study q-symmetric Caputo fractional initial value problems. It is hoped that our work will provide foundation and motivation for further studying of fractional q-symmetric difference systems.

【 授权许可】

CC BY