In this paper, a fast high order difference scheme is first proposed to solve the time fractional telegraph equation based on the ℱℒ2‐1σ formula for the Caputo fractional derivative, which reduces the storage and computational cost for calculation. A compact scheme is then presented to improve the convergence order in space. The unconditional stability and convergence in maximum norm are proved for both schemes, with the accuracy order Oτ2+h2 and Oτ2+h4, respectively. Difficulty arising from the two Caputo fractional derivatives is overcome by some detailed analysis. Finally, we carry out numerical experiments to show the efficiency and accuracy, by comparing with the ℒ2‐1σ method.
We study the exponential synchronization of coupled inertial neural networks with both discrete-time delay and distributed delay by quantized pinning controllers. Novel integral inequalities, which generalize the Jensen-based inequality, are developed by choosing appropriate weight functions in our recent work. An exponential synchronization criterion is established by applying these inequalities to analyzing a Lyapunov-Krasovskii functional which takes mixed delays into account. Numerical simulations show that the criterion can reduce conservativeness when designing parameters of the controller.
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