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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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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Electrical analogous in viscoelasticity [PDF]
, 2014 In this paper, electrical analogous models of fractional hereditary materials are introduced. Based on recent works by the authors, mechanical models of materials viscoelasticity behavior are firstly approached by using fractional mathematical ...
ALA, Guido +4 more
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A New Look at the Initial Condition Problem [PDF]
, 2022 Publisher Copyright: © 2022 by the author. Licensee MDPI, Basel, Switzerland.In this paper, some myths associated to the initial condition problem are studied and demystified.
Ortigueira, Manuel D.
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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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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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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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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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