fractional derivative

Dynamics of a fractional optimal control HBV infection model with capsids and CTL immune response

This paper deals with a fractional optimal control problem model that describes the interactions between hepatitis B virus (HBV) with HBV DNA-containing capsids, liver cells (hepatocytes), and the cytotoxic T-cell immune response.  Optimal controls represent the effectiveness of drug therapy in inhibiting viral production and preventing new infections.  The optimality system is derived and solved numerically.  Our results also show that optimal treatment strategies reduce viral load and increase the number of uninfected cells, which improves the patient's quality of lif

A nonlinear fractional partial differential equation for image inpainting

Image inpainting is an important research area in image processing.  Its main purpose is to supplement missing or damaged domains of images using information from surrounding areas.  This step can be performed by using nonlinear diffusive filters requiring a resolution of partial differential evolution equations.  In this paper, we propose a filter defined by a partial differential nonlinear evolution equation with spatial fractional derivatives.  Due to this, we were able to improve the performance obtained by known inpainting models based on partial differential equations and extend certa

Time-fractional diffusion equation for signal and image smoothing

In this paper, we utilize a time-fractional diffusion equation for image denoising and signal smoothing.  A discretization of our model is provided.  Numerical results show some remarkable results with a great performance, visually and quantitatively, compared to some well known competitive models.

Mathematical modeling of wave propagation in viscoelastic media with the fractional Zener model

The question of interest for the presented study is the mathematical modeling of wave propagation in dissipative media.  The generalized fractional Zener model in the case of dimension d (d=1,2,3) is considered.  This work is devoted to the mathematical analysis of such model: existence and uniqueness of the strong and weak solution and energy decay result which guarantees the wave dissipation.  The existence of the weak solution is shown using a priori estimates for solutions which are also presented.

Construction of Open-Loop Electromechanical System Fundamental Matrix and Its Application for Calculation of State Variables Transients

The article considers the methods of calculating the transition matrix of a dynamic system, which is based on the transient matrix representation by the matrix exponent and on the use of the system signal graph. The advantages of the transition matrix calculating using a signal graph are shown. The application of these methods to find the transition matrix demonstrated on the simple electromechanical system example.

Application of frequency stability criterion for analysis of dynamic systems with characteristic polynomials formed in j1/3 basis

This paper considers the stability of dynamical systems described by differential equations with fractional derivatives. In contrast to a number of works, where the differential equation describing the system may have a set of different values ​​of fractional derivatives, and the characteristic polynomial is formed on the basis of the least common multiple for the denominators of these indicators, this article proposes forming such a polynomial in a specific

Generalized Fokker–Planck equation for the distribution function of liquidity accumulation

By means of the method of Zubarev's nonequilibrium statistical operator, the generalized Fokker--Planck equation for the distribution function of liquidity accumulations has been obtained.  The generalized velocity and transport kernels describing dynamic correlations between liquidity accumulations of different categories of families have been determined.  The system of non-Markov transport equations for non-equilibrium average values of liquidity accumulations for different categories of families has been obtained.  Memory effects have been analyzed using the fractional calculus, which ha

Mathematical modeling of subdiffusion impedance in multilayer nanostructures

The model of impedance subdiffusion based on the Cattaneo equation in fractional derivatives in applications to multilayer nanostructures is considered. Nyquist diagrams with changes of the parameter $\tau$ (time for which the flow is delayed with respect to the concentration gradient) and the subdiffusion coefficient $D_{\alpha }$ are calculated.