An analogue of the Lyapunov inequality for an ordinary second-order differential equation with a fractional derivative and a variable coefficient [PDF]
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
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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.
M.O. Mamchuev, null null
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, 2023 Existence and uniqueness of (ω, c)−periodic solution of boundary value problem for a nonlinear system of ordinary differential equations with the quadrate of Gerasimov–Caputo operator, impulsive effects and maxima are studied. Problem is reduced to solvability of the complex system of nonlinear functional integral equations.
Yuldashev, Tursun K. +2 more
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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
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An efficient method for the analytical study of linear and nonlinear time-fractional partial differential equations with variable coefficients [PDF]
, 2023 The residual power series method is effective for obtaining approximate analytical solutions to fractional-order differential equations. This method, however, requires the derivative to compute the coefficients of terms in a series solution.
Akgül, A. +2 more
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Research of the hereditary dynamic Riccati system with modification fractional differential operator of Gerasimov-Caputo [PDF]
AIP Conference Proceedings, 2021 In this paper, we study the Cauchy problem for the Riccati differential equation with constant coefficients and a modified Gerasimov-Caputo type fractional differential operator of variable order. Using Newton's numerical algorithm, calculation curves are constructed taking into account different values of the Cauchy problem parameters. The calculation
Tverdyi, Dmitriy, Parovik, Roman
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On the solvability of equations with a distributed fractional derivative given by the Stieltjes integral [PDF]
, 2022 Linear equations in Banach spaces with a distributed fractional derivative given by the Stieltjes integral and with a closed operator A in the right-hand side are ...
Fedorov, V. E. +3 more
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Boundary value problem for a system of partial differential equations with the Dzhrbashyan–Nersesyan fractional differentiation operators [PDF]
, 2022 A boundary value problem in a rectangular domain for a system of partial differential equations with the Dzhrbashyan-Nersesyan fractional differentiation operators with constant coefficients is studied in the case when the matrix coefficients of the ...
M.O. Mamchuev
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ОБ ОДНОЙ ОБРАТНОЙ ЗАДАЧЕ ТИПА БИЦАДЗЕ-САМАРСКОГО ДЛЯ ПАРАБОЛИЧЕСКОГО УРАВНЕНИЯ ДРОБНОГО ПОРЯДКА [PDF]
, 2023 In this paper, we study a nonlocal inverse problem of the Bitsadze-Samarskii type for a degenerate parabolic equation of fractional order with the Gerasimov-Caputo operator. The spectral method is used to solve the problem. Using this method, the problem
Кадиркулов , Бахтиёр +1 more
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STUDY OF THE SINGULAR POINTS OF THE FRACTIONAL OSCILLATOR VAN DER POL-DUFFING [PDF]
Vestnik KRAUNC: Fiziko-Matematičeskie Nauki, 2019 A study is conducted on the asymptotic stability of the rest points of the fractional oscillator Van der Pol-Duffing. The fractional van der Pol-Duffing oscillator is an oscillatory system of two differential equations with fractional order derivatives ...
Е. R. Novikova
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