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20022026
most citedVariational Problems with Fractional Derivatives: Euler-Lagrange Equations

166 citations

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16 papers · 1 filter

math.AP2023★ 11 cited

Energy balance for fractional anti-Zener and Zener models in terms of relaxation modulus and creep compliance

Slađan Jelić, Dušan Zorica

Relaxation modulus and creep compliance corresponding to fractional anti-Zener and Zener models are calculated and restrictions on model parameters narrowing thermodynamical constr…

math.AP2022

Generalised solutions to linear and non-linear Schrödinger-type equations with point defect: Colombeau and non-Colombeau regimes

N. Dugandžija, A. Michelangeli, I. Vojnović

For a semi-linear Schrödinger equation of Hartree type in three spatial dimensions, various approximations of singular, point-like perturbations are considered, in the form of pote…

math.AP2022★ 3 cited

Distributed-order time-fractional wave equations

Frederik Broucke, Ljubica Oparnica

Distributed-order time-fractional wave equations appear in the modeling of wave propagation in viscoelastic media. The material characteristics of the medium are modeled through co…

math.AP2021

Some remarks on analytic pseudodifferential operators

Nenad Teofanov

We report some recent results on analytic pseudodifferential operators, also known as Wick operators. An important tool in our study is the Bargmann transform which provides a coup…

math.AP2020★ 4 cited

Stochastic parabolic equations with singular potentials

Snežana Gordić, Tijana Levajković, Ljubica Oparnica

In this work we consider a class of stochastic parabolic equations with singular space depending potential, random driving force and random initial condition. For the analysis of t…

math.AP2020★ 6 cited

Stepanov pseudo almost periodic functions and applications

K. Khalil, M. Kostić, M. Pinto

In this work, we present basic results and applications of Stepanov pseudo almost periodic functions with measures. Using only the continuity assumption, we prove a new composition…

math.AP2019★ 24 cited

Well-posedness of the fractional Zener wave equation for heterogenous viscoelastic materials

Ljubica Oparnica, Endre Süli

We explore the well-posedness of the fractional version of Zener's wave equation for viscoelastic solids, which is based on a constitutive law relating the stress tensor $\boldsymb…

math.AP2018★ 16 cited

On the characterisations of wave front sets via the short-time Fourier transform

Stevan Pilipovic, Bojan Prangoski

It is well known that the classical and Sobolev wave fronts were extended into non-equivalent global versions by the use of the short-time Fourier transform. In this very short pap…

math.AP2017★ 4 cited

Infinite order DOs: Composition with entire functions, new Shubin-Sobolev spaces, and index theorem

Stevan Pilipović, Bojan Prangoski, Jasson Vindas

We study global regularity and spectral properties of power series of the Weyl quantisation , where is a classical elliptic Shubin polynomial. For a suitable entire…

math.AP2017

Propagation of stretched exponential moments for the Kac equation and Boltzmann equation with Maxwell molecules

Milana Pavić-Čolić, Maja Tasković

We study the spatially homogeneous Boltzmann equation for Maxwell molecules, and its -dimensional model, the Kac equation. We prove propagation in time of stretched exponential…

math.AP2017★ 3 cited

Solvability and microlocal analysis of the fractional Eringen wave equation

Günther Hörmann, Ljubica Oparnica, Dušan Zorica

We discuss unique existence and microlocal regularity properties of Sobolev space solutions to the fractional Eringen wave equation, initially given in the form of a system of equa…

math.AP2016★ 15 cited

Wave equation for generalized Zener model containing complex order fractional derivatives

Teodor M. Atanacković, Marko Janev, Sanja Konjik +1

We study waves in a viscoelastic rod whose constitutive equation is of generalized Zener type that contains fractional derivatives of complex order. The restrictions following from…

math.AP2014★ 2 cited

Wave fronts via Fourier series coefficients

Snjezana Maksimovic, Stevan Pilipovic, Petar Sokoloski +1

Motivated by the product of periodic distributions, we give a new description of the wave front and the Sobolev-type wave front of a distribution i…

math.AP2011

Generalized solutions for the Euler-Bernoulli model with Zener viscoelastic foundations and distributional forces

Günther Hörmann, Sanja Konjik, Ljubica Oparnica

We study the initial-boundary value problem for an Euler-Bernoulli beam model with discontinuous bending stiffness laying on a viscoelastic foundation and subjected to an axial for…

math.AP2011

Waves in fractional Zener type viscoelastic media

Sanja Konjik, Ljubica Oparnica, Dušan Zorica

Classical wave equation is generalized for the case of viscoelastic materials obeying fractional Zener model instead of Hooke's law. Cauchy problem for such an equation is studied:…

math.AP2006★ 1 cited

Singular shock waves in interactions

Marko Nedeljkov

n a number of papers it was shown that there are one-dimensional systems such that they contain solutions with, so called, overcompressive singular shock waves besides the usual el…