The main aim of the paper is to present an algorithm solve approximately initial value problems for a scalar non-linear fractional differential equation with generalized proportional derivative on finite interval. condition connected one sided Lipschitz right hand side part given equation. An iterative scheme, based appropriately defined mild lower and upper solutions, provided. Two monotone se...

This paper studies the leader-following consensus problem of nonlinear multi-agent systems (MAS) with one-sided Lipschitz conditions under directed graph, and a novel observer-based distributed tracking protocol that only utilizes relative output information adjacent agents is proposed. To avoid disadvantage solving Laplace matrix eigenvalues, fully adaptive scheme constructed. The sufficient f...

we investigate compact composition operators on ceratin lipschitzspaces of analytic functions on the closed unit disc of the plane.our approach also leads to some results about compositionoperators on zygmund type spaces.

Numerous state-feedback and observer designs for nonlinear dynamic systems (NDS) have been developed in the past three decades. These assume that NDS nonlinearities satisfy one of following function set classifications: bounded Jacobian, Lipschitz continuity, one-sided Lipschitz, quadratic inne...

This article studies the cluster synchronization problem of coupled nonlinear systems with directed topology and competitive relationships. We assume that nodes within same have intrinsic dynamics, while dynamics belonging to different clusters are different. In cluster, there only exist cooperative relationships, may relationships among clusters. Under assumptions dynamic each node satisfies o...

in this paper, we consider a class of time-dependent neutral stochastic evolution equations with the infinite delay and a fractional brownian motion in a hilbert space. we establish the existence and uniqueness of mild solutions for these equations under non-lipschitz conditions with lipschitz conditions being considered as a special case. an example is provided to illustrate the theory

‎in this work we prove malliavin differentiability for the solution to an sde with locally lipschitz and semi-monotone drift‎. ‎to prove this formula‎, ‎we construct a sequence of sdes with globally lipschitz drifts and show that the $p$-moments of their malliavin derivatives are uniformly bounded‎.