Mathematical Models of Oscillators with Memory [PDF]
, 2018 The chapter proposes a mathematical model for a wide class of hereditary oscillators, which is a Cauchy problem in the local formulation. As an initial model equation, an integrodifferential equation of Voltaire type was introduced, which was reduced by ...
Parovik, Roman Ivanovich
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Criteria for integro-differential modeling of plane-parallel flow of viscous incompressible fluid [PDF]
, 2023 For a liquid with a nonmonotonic flow curve in the stationary case in the region of the descending branch, setting the velocity at the boundary does not uniquely determine the shear stress, strain rate distribution, and velocity profile that arise since ...
Abdullaev A. A. +2 more
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The explicit formula for solution of anomalous diffusion equation in the multi-dimensional space [PDF]
, 2020 This paper intends on obtaining the explicit solution of n-dimensional anomalous diffusion equation in the infinite domain with non-zero initial condition and vanishing condition at infinity.
Durdiev, D., Shishkina, E., Sitnik, S.
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ON THE NUMERICAL SOLUTION OF EQUATIONS FRACTAL OSCILLATOR WITH VARIABLE ORDER FRACTIONAL OF TIME [PDF]
Vestnik KRAUNC: Fiziko-Matematičeskie Nauki, 2014 We propose a model of a fractal oscillator with variable fractional order. Received and investigated by numerical solution of the model.
R.I. Parovik
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Recent applications of fractional calculus to science and engineering
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 54, Page 3413-3442, 2003., 2003 This paper deals with recent applications of fractional calculus to dynamical systems in control theory, electrical circuits with fractance, generalized voltage divider, viscoelasticity, fractional‐order multipoles in electromagnetism, electrochemistry, tracer in fluid flows, and model of neurons in biology.
Lokenath Debnath
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ON THE INVERSE PROBLEM OF THE BITSADZE–SAMARSKII TYPE FOR A FRACTIONAL PARABOLIC EQUATION [PDF]
, 2023 In this paper, the inverse problem of the Bitsadze–Samarsky type is studied for a fractional order equation with a Hadamard–Caputo fractional differentiation operator. The problem is solved using the spectral method.
B. J. Kadirkulov +2 more
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Quasilinear Fractional Order Equations and Fractional Powers of Sectorial Operators
Fractal and Fractional, 2023 The fractional powers of generators for analytic operator semigroups are used for the proof of the existence and uniqueness of a solution of the Cauchy problem to a first order semilinear equation in a Banach space. Here, we use an analogous construction
Vladimir E. Fedorov +2 more
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Hereditary Mathematical Model of the Dynamics of Radon Accumulation in the Accumulation Chamber
Mathematics, 2023 Mathematical modeling is used to study the hereditary mechanism of the accumulation of radioactive radon gas in a chamber with gas-discharge counters at several observation points in Kamchatka.
Dmitrii Tverdyi +2 more
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Special functions as solutions to the Euler-Poisson-Darboux equation with a fractional power of the Bessel operator [PDF]
, 2021 In this paper, we consider fractional ordinary differential equations and the fractional Euler-Poisson-Darboux equation with fractional derivatives in the form of a power of the Bessel differential operator.
Dzarakhohov, A. +2 more
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NUMERICAL ANALYSIS OF THE CAUCHY PROBLEM FOR A WIDE CLASS FRACTAL OSCILLATORS [PDF]
Vestnik KRAUNC: Fiziko-Matematičeskie Nauki, 2018 The Cauchy problem for a wide class of fractal oscillators is considered in the paper and its numerical investigation is carried out using the theory of finite-difference schemes.
R. I. Parovik
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