Results 11 to 20 of about 13,021 (91)

The optimization problem for determining the functional dependence of the variable order of the fractional derivative of the Gerasimov-Caputo type

Вестник КРАУНЦ. Физико-математические науки
При решении задач математического моделирования часто приходится обращаться к теории интегрально-дифференциального исчисления. С ее помощью можно описывать динамические процессы самой разной природы. Использование аппарата дробных производных позволяет уточнить некоторые из этих моделей за счет учета в уравнениях эффекта памяти.
Tvërdyĭ, Dmitriĭ Aleksandrovich, Parovik, Roman Ivanovich   +1 more
openaire   +2 more sources

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
doaj   +2 more sources

On the Numerical Solution of the Basic Equation of Wave Mechanics with the Gerasimov – Caputo Fractional Derivative

Yugra State University Bulletin
Subject of research: initial-boundary value problem for the fundamental equation of fractional wave mechanics with fractional Gerasimov – Kaputo time derivative and the influence of the numerical solution parameters on the accuracy and stability of quantum system modeling.
Georgy A. Neverov, Natalia D. Ivanova
openaire   +2 more sources

Hille–Yosida-Type Theorem for Fractional Differential Equations with Dzhrbashyan–Nersesyan Derivative

Fractal and Fractional
It is a well-known fact that the Dzhrbashyan–Nersesyan fractional derivative includes as particular cases the fractional derivatives of Riemann–Liouville, Gerasimov–Caputo, and Hilfer.
Vladimir E. Fedorov, Wei-Shih Du, Marko Kostić, Marina V. Plekhanova, Darya V. Melekhina   +4 more
doaj   +2 more sources

An Analysis of the Computational Complexity and Efficiency of Various Algorithms for Solving a Nonlinear Model of Radon Volumetric Activity with a Fractional Derivative of a Variable Order

Computation
The article presents a study of the computational complexity and efficiency of various parallel algorithms that implement the numerical solution of the equation in the hereditary α(t)-model of radon volumetric activity (RVA) in a storage chamber.
Dmitrii Tverdyi
doaj   +2 more sources

Analysis of a Finite Difference Method for a Time-Fractional Black–Scholes Equation

Fractal and Fractional
The goal of this paper is to give an error analysis of a finite difference method for a time-fractional Black–Scholes equation with weakly singular solutions.
Qingzhao Li, Chaobao Huang, Tao Sun, Hu Chen   +3 more
doaj   +2 more sources

Application of the Riccati hereditary mathematical model to the study of the dynamics of radon accumulation in the storage chamber [PDF]

EPJ Web of Conferences, 2021
The article proposes a mathematical model of radon accumulation in a chamber, which takes into account the hereditary properties of the environment in which radon migrates.
Tverdyi Dmitryi, Parovik Roman, Makarov Evgeniy, Firstov Pavel, Alimova Nazira   +4 more
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

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

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