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N. A. Aliev

Publications and source records attributed to N. A. Aliev.

6 recordsLinked to original sources
arXiv2020

Analytical construction of regulators for oscillatory systems with liquid dampers

A mathematical model of oscillatory systems control with liquid dampers is considered which differs from the classical ones by replacing the first derivative of such a fractional derivative that is between numbers 0 and 2 other than unity. Using the methods of constructing Letov controllers, a control law is constructed that ensures the asymptotic stability of the closed system and minimizes the quadratic functional. The results are illustrated by a specific numerical example.

math.DS↗
arXiv2019

Method of discretizing of fractional-derivative linear systems of ordinary differential equations with constant coefficients

An exact discretization method is being developed for solving linear systems of ordinary fractional-derivative differential equations with constant matrix coefficients (LSOFDDECMC). It is shown that the obtained linear discrete system in this case does not have constant matrix coefficients. Further, this method is compared with the known approximate method. The above scheme is developed for arbitrary linear systems with piecewise constant perturbations. The results are applied to the discretization of linear controlled systems and are illustrated with numerical examples.

math.DS↗
arXiv2018

Solving the linear fractional derivatives ordinary differential equations with constant matrix coefficients

The Cauchy problem for fractional derivatives linear systems of ordinary differential equations with constant coefficients is considered, where at first the analytic expressions are given through the matrix exponent of its corresponding solution. On the basis of the obtained results the conditions are given, providing the asymptotic stability of the initial system. The results are illustrated on the numerical example, where it is shown that when the order of the fractional derivative tends to unity, so the solution tends to the corresponding exponential function.

math.DS↗
arXiv2018

Transformation Mittag-Lefler function to an exponential function and its some applications to problems with a fractional derivative

In this work at first the relation the Mittag-Lefler function to the exponential is given. The results are applied to the construction of the solution of Cauchy problem for ordinary linear operator differential equations with constant coefficients and fractional derivatives. On the example is shown that when the order of the derivatives (fractional) approaches to integers the results coincide with the classical.

math.DS↗
arXiv2008

Investigation of solutions of boundary value problems for a composite type equation with non-local boundary conditions

Since the order of elliptic type model equation (Laplace equation) is two [1], [2], then it is natural the order of composite type model equation must be [3] [4] [5] three. At each point of the domain under consideration these equations have both real and complex characteristics. Notice that a boundary value problem for a composite type equation of second order first appeared in the paper [6]. The method for investigating the Fredholm property of boundary value problems is distinctive and belongs to one of the authors of the present paper.

math.AP↗