Results 41 to 50 of about 244 (107)
Mathematical Models of Oscillators with Memory [PDF]
, 2018 The chapter proposes a mathematical model for a wide class of hereditary oscillators, which is a Cauchy problem in the local formulation. As an initial model equation, an integrodifferential equation of Voltaire type was introduced, which was reduced by ...
Parovik, Roman Ivanovich
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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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A general phase-field model for fatigue failure in brittle and ductile solids [PDF]
, 2021 In this work, the phase-field approach to fracture is extended to model fatigue failure in high- and low-cycle regime. The fracture energy degradation due to the repeated externally applied loads is introduced as a function of a local energy accumulation
Aldakheel, Fadi +4 more
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, 2012 In this note we analyze a model for a unidirectional unsteady flow of a viscous incompressible fluid with time dependent viscosity. A possible way to take into account such behaviour is to introduce a memory formalism, including thus the time dependent ...
Garra, Roberto, Polito, Federico
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An Historical Perspective on Fractional Calculus in Linear Viscoelasticity
, 2012 The article provides an historical survey of the early contributions on the applications of fractional calculus in linear viscoelasticty. The period under examination covers four decades, since 1930's up to 1970's and authors are from both Western and ...
Mainardi, Francesco
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Application of Fractional Calculus to Oil Industry [PDF]
, 2017 In this chapter, we present a discussion about the practical application of the fractal properties of the medium in the mathematical model through the use of fractional partial derivatives.
Fuentes, Carlos +3 more
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Explicit Solutions to Fractional Stefan-like problems for Caputo and Riemann-Liouville Derivatives [PDF]
, 2020 Two fractional two-phase Stefan-like problems are considered by using Riemann-Liouville and Caputo derivatives of order $\alpha \in (0, 1)$ verifying that they coincide with the same classical Stefan problem at the limit case when $\alpha=1$.
Caruso, Nahuel +2 more
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On the generalized Laplace transform [PDF]
, 2021 This article belongs to the Special Issue Discrete and Fractional Mathematics: Symmetry and Applications.In this paper we introduce a generalized Laplace transform in order to work with a very general fractional derivative, and we obtain the properties ...
Bosch, Paul +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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Задача Дирихле для обобщенного уравнения Лаврентьева-Бицадзе с дробной производной Герасимова-Капуто [PDF]
, 2020 Исследована задача Дирихле для дифференциального уравнения в частных производных второго порядка с дробной производной по временной переменной в прямоугольной области. В случае если порядок дробного дифференцирования равен двум, рассматриваемое уравнение
Масаева, О. Х.
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