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Razumikhin-type stability theorems for one class of coupled system of time-delay fractional-order differential equations on network

In this paper, the stability problem of the new coupled model constructed by two time-delay fractional-order differential equations for every vertex is studied. Firstly, by using the method of constructing Lyapunov functions based on graph-theoretical approach for coupled systems, Razumikhin-type global uniform stability and global uniform asymptotical stability theorems are obtained for the coupling model with time delays. Secondly and finally, an example is given to illustrate the applications of main results.