This paper studies the finite-time synchronization problem of fractional-order stochastic memristive bidirectional associative memory neural networks (MBAMNNs) with discontinuous jumps. A novel criterion for finite-time synchronization is obtained by utilizing the properties of quadratic fractional-order Gronwall inequality with time delay and the comparison principle. This criterion provides a new approach to analyze the finite-time synchronization problem of neural networks with stochasticity. Finally, numerical simulations are provided to demonstrate the effectiveness and superiority of the obtained results.

In this paper, we first propose the concepts of $(\zeta ,\eta ,\lambda ,\pi )$-generalized hybrid multi-valued mappings, the set of all the common attractive points ($C{A}_{f,g}$) and the set of all the common strongly attractive points ($C_s{A}_{f,g}$), respectively for the multi-valued mappings f and g in a CAT(0) space. Moreover, we give some elementary properties in regard to the sets $A_f$, $F_f$ and $C{A}_{f,g}$ for the multi-valued mappings f and g in a complete CAT(0) space. Furthermore, we present a weak convergence theorem of common attractive points for two $(\zeta ,\eta ,\lambda ,\pi )$-generalized hybrid multi-valued mappings in the above space by virtue of Banach limits technique and Ishikawa iteration respectively. Finally, we prove strong convergence of a new viscosity approximation method for two $(\zeta ,\eta ,\lambda ,\pi )$-generalized hybrid multi-valued mappings in CAT(0) spaces, which also solves a kind of variational inequality problem.

In this paper, the problem of the uniform stability for a class of fractional-order fuzzy impulsive complex-valued neural networks with mixed delays in infinite dimensions is discussed for the first time. By utilizing fixed-point theory, theory of differential inclusion and set-valued mappings, the uniqueness of the solution of the above complex-valued neural networks is derived. Subsequently, the criteria for uniform stability of the above complex-valued neural networks are established. In comparison with related results, we do not need to construct a complex Lyapunov function, reducing the computational complexity. Finally, an example is given to show the validity of the main results.

Our paper is devoted to the issue of the existence and uniqueness of common fixed points for two mappings in complete b-metric spaces by virtue of the new functions F and $\theta$, respectively. Moreover, two specific examples to indicate the validity of our results are also given. Eventually, the generalized forms of Jungck fixed point theorem in the above spaces is investigated. Different from related literature, the conditions that the function F needs to satisfy are weakened, and F only needs to be non-decreasing in this paper. To some extent, our conclusions and methods improve the results of previous literature.

This paper studies the finite-time synchronization problem of fractional-order stochastic memristive bidirectional associative memory neural networks (MBAMNNs) with discontinuous jumps. A novel criterion for finite-time synchronization is obtained by utilizing the properties of quadratic fractional-order Gronwall inequality with time delay and the comparison principle. This criterion provides a new approach to analyze the finite-time synchronization problem of neural networks with stochasticity. Finally, numerical simulations are provided to demonstrate the effectiveness and superiority of the obtained results.

In this paper, the problem of the existence and uniqueness of solutions for a nonlinear fractional-order coupled delayed system with a new kind of boundary condition is studied. For this reason, we transform the above problem into an equivalent fixed point problem using the integral operator. Moreover, by applying fixed point theorems, a novel set of sufficient conditions that guarantee the existence and uniqueness of solutions of the coupled system is derived. Eventually, an example is presented to illustrate the effectiveness of the obtained results.