In this paper, a time fractional diffusion equation on a finite domain is con- sidered. The time fractional diffusion equation is obtained from the standard diffusion equation by replacing the first order time derivative by a fractional derivative of order 0 < a< 1 (in the Riemann-Liovill or Caputo sence). In equation that we consider the time fractional derivative is in...

This paper presents a new observer based fuzzy terminal sliding mode controller design for a class of fractional order nonlinear systems. Robustness against uncertainty and disturbance, the stability of the close loop system and the convergence of both the tracking and observer errors to zero are the merits of the proposed the observer and the controller. The high gain observer is applied to es...

In the present paper, stability and convergence properties of linear multistep methods are investigated. The attention is focused on parabolic problems and variable stepsizes. Under weak assumptions on the method and the stepsize sequence an asymptotic stability result is shown. Further, stability bounds for linear nonautonomous parabolic problems with Hölder continuous operator are given. With...

We study the stability of convergence of the ChristoffelDarboux kernel, associated with a compactly supported measure, to the sine kernel, under perturbations of the Jacobi coefficients of the measure. We prove stability under variations of the boundary conditions and stability in a weak sense under ` and random ` diagonal perturbations. We also show that convergence to the sine kernel at x imp...

Adaptive equalizer is important in transmission of wireless communication. The equalizer using least mean square (LMS) algorithm is adopted. Simulation results show that step size influences the algorithm convergence and stability, which will significantly affect the performance of adaptive equalizer. The requirement of step for convergence speed, time-varying tracking accuracy and convergence ...

This paper is concerned with the stability and numerical analysis of solution to highly nonlinear stochastic differential equations with jumps. By the Itô formula, stochastic inequality and semi-martingale convergence theorem, we study the asymptotic stability in the pth moment and almost sure exponential stability of solutions under the local Lipschitz condition and nonlinear growth condition....