Abstract Aiming at the problems of image edge blur and detail loss in most denoising models, an model based on improved fractional calculus is proposed. Through classification noise, integer order PDE discussed. Based mathematical theory calculus, The by combining texture detection operator, gray value smoothing factor fast algorithm. simulation experiment carried out MATLAB platform. results s...

In this paper studies the exponential stability result is derived for second-order fractional stochastic integro-differential equations (FSIDEs) driven by sub-fractional Brownian motion (sub-fBm). By constructing a successive approximation method, we present pth moment of FSIDEs using analysis techniques and calculus (FC). At last, an example demonstrated to illustrate obtained theoretical resu...

In this paper, a new approach to stability for fractional order control system is proposed. Here a dynamic system whose behavior can be modeled by means of differential equations involving fractional derivatives. Applying Laplace transforms to such equations, and assuming zero initial conditions, causes transfer functions with no integer powers of the Laplace transform variable s to appear. In ...

Fractional order calculus can represent systems with high-order dynamics and complex nonlinear phenomena using few coefficients, since the arbitrary order of the derivatives provides an additional degree of freedom to fit a specific behavior. Numerous mathematicians have contributed to the history of fractional calculus by attempting to solve a fundamental problem to the best of their understan...

System identification refers to estimation of process parameters and is a necessity in control theory. Physical systems usually have varying parameters. For such processes, accurate identification is particularly important. Online identification schemes are also needed for designing adaptive controllers. Real processes are usually of fractional order as opposed to the ideal integral order model...

Fractional derivative or fractional calculus plays a significant role in theoretical modeling of scientific and engineering problems. However, only relatively low order fractional derivatives are used at present. In general, it is not obvious what role a high fractional derivative can play and how to make use of arbitrarily high-order fractional derivatives. This work introduces arbitrarily hig...

To accurately describe the deformation characteristics of clay under long-term cyclic load, based on fractional calculus theory, elastoplastic theory and basic element model, a variable-order dynamic model designed to predict accumulative strain was exhibited. Firstly, load separated into static alternating in accordance with characteristics, analyzed. Then, basis Abel dashpot rheological expre...