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A difference method for solving the nonlinear qfactional differential equations on time scale
The qfractional 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 qderivative ^cD_q^α x(t) on the time scale set T_q with order 0<α<1 and scale index 0<q<1. We establish a rigours truncation error boundness and prove that this difference formula is unconditionally stable. Then, we consider the difference method for solving the initial problem of qfractional differential equation: ^cD_q^α x(t)=f(t,x(t)) on the time scale set. We prove the unique existence and stability of the difference solution and give the convergence analysis. Numerical experiments show the effectiveness and high accuracy of the proposed difference method.
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