#### A difference method for solving the nonlinear $q$-factional differential equations on time scale

##### Tie Zhang

The $q$-fractional differential equation usually describe the physics process imposed on the time scale set $T_q$. In this paper, we first propose a difference formula for discretizing the fractional $q$-derivative $^cD_q^\alpha x(t)$ on the time scale set $T_q$ with order $0<\alpha<1$ and scale index \$0

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