相关论文: Non-Standard Extensions of Gradient Elasticity: Fr…

In this paper we consider extensions of the gradient elasticity models proposed earlier by the second author to describe materials with fractional non-locality and fractality using the techniques developed recently by the first author. We…

An extension of gradient elasticity through the inclusion of spatial derivatives of fractional order to describe power-law type of non-locality is discussed. Two phenomenological possibilities are explored. The first is based on the Caputo…

Non-local elasticity models in continuum mechanics can be treated with two different approaches: the gradient elasticity models (weak non-locality) and the integral non-local models (strong non-locality). This article focuses on the…

Using a generalization of vector calculus for space with non-integer dimension, we consider elastic properties of fractal materials. Fractal materials are described by continuum models with non-integer dimensional space. A generalization of…

Fractional dynamics is a field of study in physics and mechanics investigating the behavior of objects and systems that are characterized by power-law non-locality, power-law long-term memory or fractal properties by using integrations and…

Fractional calculus is an effective tool in incorporating the effects of non-locality and memory into physical models. In this regard, successful applications exist rang- ing from signal processing to anomalous diffusion and quantum…

The paper discusses the characteristic properties of fractional derivatives of non-integer order. It is known that derivatives of integer orders are determined by properties of differentiable functions only in an infinitely small…

The study of systems with memory requires methods which are different from the methods used in regular dynamics. Systems with power-law memory in many cases can be described by fractional differential equations, which are…

This study presents a fractional-order continuum mechanics approach that allows combining selected characteristics of nonlocal elasticity, typical of classical integral and gradient formulations, under a single frame-invariant framework.…

Viscoelasticity and related phenomena are of great importance in the study of mechanical properties of material especially, biological materials. Certain materials show some complex effects in mechanical tests, which cannot be described by…

The derivation of nonlocal strong forms for many physical problems remains cumbersome in traditional methods. In this paper, we apply the variational principle/weighted residual method based on nonlocal operator method for the derivation of…

We show a relation between fractional calculus and fractals, based only on physical and geometrical considerations. The link has been found in the physical origins of the power-laws, ruling the evolution of many natural phenomena, whose…

With the discovery of new superconductors there was a running to find the justifications for the new properties found in these materials. In order to describe these new effects some theories were adapted and some others have been tried. In…

Lattice models with long-range interactions of power-law type are suggested as a new type of microscopic model for fractional non-local elasticity. Using the transform operation, we map the lattice equations into continuum equation with…

Transport equations with a nonlocal velocity field have been introduced as a continuum model for interacting particle systems arising in physics, chemistry and biology. Fractional time derivatives, given by convolution integrals of the…

Anomalous relaxation and diffusion processes have been widely characterized by fractional derivative models, where the definition of the fractional-order derivative remains a historical debate due to the singular memory kernel that…

The aim of this paper is to bring together two approaches to non-conservative systems -- the generalized variational principle of Herglotz and the fractional calculus of variations. Namely, we consider functionals whose extrema are sought,…

We obtain Euler-Lagrange equations, transversality conditions and a Noether-like theorem for Herglotz-type variational problems with Lagrangians depending on generalized fractional derivatives. As an application, we consider a damped…

Field equations with time and coordinates derivatives of noninteger order are derived from stationary action principle for the cases of power-law memory function and long-range interaction in systems. The method is applied to obtain a…

A lattice model with a spatial dispersion corresponding to a power-law type is suggested. This model serves as a microscopic model for elastic continuum with power-law non-locality. We prove that the continuous limit maps of the equations…