Novel Caputo fractional differential approach and hybrid control scheme for finite-time synchronization of nonidentical delayed reaction–diffusion neural networks

This work focuses on the finite-time synchronization (F-TS) for nonidentical delayed neural networks (DNNs) including Caputo fractional partial differential operator and reaction–diffusion terms. A novel F-TS lemma is proposed by constructing a new Caputo differential inequality. Applying the new lemma and designing two hybrid controllers with time delay and the sign function, the F-TS criteria on the introduced Caputo reaction–diffusion nonidentical DNNs under the Neumann boundary condition are derived by making use of the Filippov differential inclusion, Green's theorem, and fractional Razumikhin theorem. The conditions are expressed through the algebraic inequality which can greatly decrease the computation in checking the F-TS performance. Moreover, the validity and correctness of the F-TS results are illustrated by selecting various orders, spatial positions, and diffusion parameters.