A discrete mechanical model of fractional hereditary materials [PDF]
, 2013 Fractional hereditary materials are characterized for the presence, in the stress-strain relations, of fractional-order operators with order beta a[0,1]. In Di Paola and Zingales (J. Rheol.
DI PAOLA, Mario +2 more
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Integro-differential equations with bounded operators in Banach spaces [PDF]
, 2022 The paper investigates integro-differential equations in Banach spaces with operators, which are a composition of convolution and differentiation operators.
A.D. Godova, B.T. Kien, V.E. Fedorov
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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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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 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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, 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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Ідентифікація параметрів однієї дробово-диференціальної моделі міграції розчинних речовин [PDF]
, 2019 Розглядається задача ідентифікації параметрів моделі у випадку математичного моделювання дробово-диференціальної динаміки аномального процесу конвективної дифузії розчинних речовин при профільній усталеній фільтрації ґрунтових вод з вільною поверхнею ...
Богаєнко, В.А. +2 more
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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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