Results 41 to 50 of about 47,860 (125)
Mathematics, 2020 We consider the principle of least action in the context of fractional calculus. Namely, we derive the fractional Euler–Lagrange equation and the general equation of motion with the composition of the left and right fractional derivatives defined on ...
Liana Eneeva +2 more
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Fractal and Fractional, 2022 In this study, the model Riccati equation with variable coefficients as functions, as well as a derivative of a fractional variable order (VO) of the Gerasimov-Caputo type, is used to approximate the data for some physical processes with saturation.
Dmitriy Tverdyi, Roman Parovik
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About one differential model of dynamics of groundwater [PDF]
, 2023 When modeling the flow of groundwater and streams together, two different approaches are used, using hydraulic and hydrological models as channel flow models. The former is based on mathematical equations of water movement in open channels.
Abdullayev A. A. +2 more
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Vestnik KRAUNC: Fiziko-Matematičeskie Nauki, 2023 The article presents a software implementation of a parallel efficient and fast computational algorithm for solving the Cauchy problem for a nonlinear differential equation of a fractional variable order.
Tverdyi, D.A. +3 more
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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
wiley +1 more source
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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