Abstract
Gronwall inequalities are widely used in analytical science, especially in ordinary or fractional differential systems. In this paper, a tempered Gronwall inequality is proposed and applied to tempered fractional system. By the tempered Gronwall inequality, dependences of the solution of tempered fractional systems on initial value, fractional order and tempered parameter are obtained. Finally, a new tempered fractional chaotic system is proposed to show the validity of the dependences.
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