Results 11 to 20 of about 244 (107)

Some Aspects of Numerical Analysis for a Model Nonlinear Fractional Variable Order Equation

Mathematical and Computational Applications, 2021
The article proposes a nonlocal explicit finite-difference scheme for the numerical solution of a nonlinear, ordinary differential equation with a derivative of a fractional variable order of the Gerasimov–Caputo type.
Roman Parovik, Dmitriy Tverdyi
doaj   +1 more source

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, Evgeny Makarov, Roman Parovik   +2 more
doaj   +1 more source

Application of the Fractional Riccati Equation for Mathematical Modeling of Dynamic Processes with Saturation and Memory Effect

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
doaj   +1 more source

Parallelization of a Numerical Algorithm for Solving the Cauchy Problem for a Nonlinear Differential Equation of Fractional Variable Order Using OpenMP Technology

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., Parovik, R.I., Hayotov, A.R., Boltaev, A.K.   +3 more
doaj   +1 more source

On Strongly Continuous Resolving Families of Operators for Fractional Distributed Order Equations

Fractal and Fractional, 2021
The aim of this work is to find by the methods of the Laplace transform the conditions for the existence of a strongly continuous resolving family of operators for a linear homogeneous equation in a Banach space with the distributed Gerasimov–Caputo ...
Vladimir E. Fedorov, Nikolay V. Filin
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An Initial Problem for a Class of Weakly Degenerate Semilinear Equations with Lower Order Fractional Derivatives

Известия Иркутского государственного университета: Серия "Математика", 2021
An initial value problem is studied for a class of evolutionary equations with a weak degeneration, which are nonlinear with respect to lower order fractional Gerasimov – Caputo derivatives.
G.D. Baybulatova, M.V. Plekhanova
doaj   +1 more source

An analogue of the Lyapunov inequality for an ordinary second-order differential equation with a fractional derivative and a variable coefficient

Қарағанды университетінің хабаршысы. Математика сериясы, 2022
This paper studies an ordinary second-order differential equation with a fractional differentiation operator in the sense of Riemann-Liouville with a variable coefficient.
B.I. Efendiev
doaj   +1 more source

The Regularized Mesh Scheme to Solve Quasilinear Parabolic Equation with Time-Fractional Derivative [PDF]

, 2021
A quasilinear parabolic problem with a time fractional derivative of the Caputo type and mixed boundary conditions is considered. The coefficients of the elliptic operator depend on the gradient of the solution, and this operator is uniformly monotone ...
Laitinen, E., Lapin, A. V.
core   +1 more source

Дробно-дифференциальная модель физических процессов с насыщением и ее применение к описанию динамики COVID-19

Vestnik KRAUNC: Fiziko-Matematičeskie Nauki, 2022
В этой статье была использована дробно-дифференциальная модель физических процессов с насыщением для описания динамики летальных исходов инфекции COVID-19.
Твёрдый, Д.А., Паровик, Р.И.   +1 more
doaj   +1 more source

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, Marko Kostić, Tatyana A. Zakharova   +2 more
doaj   +1 more source