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
Нелокальная краевая задача для уравнения с производными дробного порядка с различными началами
Vestnik KRAUNC: Fiziko-Matematičeskie Nauki, 2023 Рассматривается линейное обыкновенное дифференциальное уравнение дробного порядка с композицией лево- и правосторонних операторов дробных производных в главной части.
Энеева, Л.М.
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Fractional Diffusion–Wave Equation with Application in Electrodynamics
Mathematics, 2020 We consider a diffusion–wave equation with fractional derivative with respect to the time variable, defined on infinite interval, and with the starting point at minus infinity.
Arsen Pskhu, Sergo Rekhviashvili
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Integrated Resolving Functions for Equations with Gerasimov–Caputo Derivatives
Symmetry, 2023 The concept of a β-integrated resolving function for a linear equation with a Gerasimov–Caputo fractional derivative is introduced into consideration. A number of properties of such functions are proved, and conditions for the solvability of the Cauchy problem to linear homogeneous and inhomogeneous equations are found in the case of the existence of a
Vladimir E. Fedorov +2 more
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A Class of Quasilinear Equations with Distributed Gerasimov–Caputo Derivatives
Mathematics, 2023 Quasilinear equations in Banach spaces with distributed Gerasimov–Caputo fractional derivatives, which are defined by the Riemann–Stieltjes integrals, and with a linear closed operator A, are studied. The issues of unique solvability of the Cauchy problem to such equations are considered.
Vladimir E. Fedorov, Nikolay V. Filin
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Cauchy problem for a system of equations with the partial Gerasimov – Caputo derivatives
REPORTS ADYGE (CIRCASSIAN) INTERNATIONAL ACADEMY OF SCIENCES, 2021 For the system of equations with the partial Gerasimov – Caputo derivatives, a general representation of regular in a rectangular domain solutions is constructed. Cauchy problem is investigated. Theorems of existence and uniqueness of the solution are proved.
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Analysis of a Finite Difference Method for a Time-Fractional Black–Scholes Equation
Fractal and FractionalThe 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 +3 more
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The second boundary value problem in a half-strip for a B-parabolic equation with the Gerasimov–Caputo time derivative [PDF]
Вестник КРАУНЦ. Физико-математические науки, 2020 В работе исследуется вторая краевая задача в полуполосе для параболического уравнения с оператором Бесселя, действующим по пространственной переменной, и частной производной Герасимова–Капуто по времени. Доказаны теоремы существования и единственности решения рассматриваемой задачи.
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The existence of chaotic regimes of the fractional analogue of the Duffing-type oscillator
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2019 In this paper, we study the chaotic regimes of the fractional Duffing oscillator. To do this, using the Wolf algorithm with Gram-Schmidt orthogonalization, we calculated the spectra of maximum Lyapunov exponents depending on the values of the control ...
Roman Ivanovich Parovik
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