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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Models of Delay Differential Equations [PDF]
, 2022 This book gathers a number of selected contributions aimed at providing a balanced picture of the main research lines in the realm of delay differential equations and their applications to mathematical modelling.
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Mathematics, 2023 The numerical solution for fractional dynamics problems can create a high computational load, which makes it necessary to implement efficient algorithms for their solution.
Dmitrii Tverdyi, Roman Parovik
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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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A Modified Fractional Derivative and its Application to Fractional Vibration Equation [PDF]
, 2016 In this paper, a new modified definition of the fractional derivative is presented. The Laplace transform of the modified fractional derivative involves the initial values of the integer-order derivatives, but does not involve the initial values of the ...
Duan, Jun-Sheng
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Mathematical Modeling of Linear Fractional Oscillators
Mathematics, 2020 In this work, based on Newton’s second law, taking into account heredity, an equation is derived for a linear hereditary oscillator (LHO). Then, by choosing a power-law memory function, the transition to a model equation with Gerasimov–Caputo fractional ...
Roman Parovik
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Третья краевая задача для нагруженного уравнения теплопроводности с дробной производной Капуто [PDF]
, 2020 Recently, to describe various mathematical models of physical processes, fractional differential calculus has been widely used. In this regard, much attention is paid to partial differential equations of fractional order, which are a generalization of ...
M. Kh. Beshtokov +3 more
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