Finite-time synchronization of fuzzy neural networks with fractional order

This paper discusses the finite-time synchronization (FTS) for a class of fractional-order fuzzy neural networks (FOFNNs). First, a general fractional differential inequality is developed, which provides new approaches for dealing with $l_{1}f^{-\beta}(t), (\beta >0)$ . Furthermore, a nonlinear fractional-order finite time inequality $_{t_{0}}^{c}D_{t}^{\alpha}V(t)\leq -l_{1}V^{-\beta}(t)-l_{3}V^{- \gamma}(t)$ is also established. Next, three controllers are designed, namely two feedback nonlinear controllers and adaptive controller. Then, using mathematical analysis and the newly established inequality, several easily-validated algebraic conditions are derived to guarantee the FTS of FOFNNs. Moreover, the paper effectively estimates the upper bound of the settling time for FTS. Finally, a numerical example is provided to demonstrate the validity of the theoretical results.