Related papers: On variable-order fractional linear viscoelasticit…
We describe a general operational method that can be used in the analysis of fractional initial and boundary value problems with additional analytic conditions. As an example, we derive analytic solutions of some fractional generalisation…
In this work, a new collocation approach using a combination of a wavelet operational matrix method and the exponential spline interpolation is proposed to solve the time-fractional convection-diffusion equation with variable coefficients.…
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…
We suggest a generalization of vector calculus for the case of non-integer dimensional space. The first and second orders operations such as gradient, divergence, the scalar and vector Laplace operators for non-integer dimensional space are…
The one-dimensional fractional derivative Maxwell model (e.g. Palade et al. Rheol. Acta 35, 265, 1996), of importance in modeling the linear viscoelastic response in the glass transition region, has been generalized in Palade et al. Int. J.…
Over the last decade, it has been demonstrated that many systems in science and engineering can be modeled more accurately by fractional-order than integer-order derivatives, and many methods are developed to solve the problem of fractional…
An analysis of a fractional cubic differential equation is presented, which is a generalization of different versions of fractional logistic equations, in order to obtain simpler numerical methods that globalize and extend the results…
We formulate a phase field crack growth model for mode III fracture in a Maxwell-type viscoelastic material. To describe viscoelastic relaxation, a field variable of viscously flowed strain is employed in addition to a displacement field…
We analyze matrix convex functions of a fixed order defined on a real interval by differential methods as opposed to the characterization in terms of divided differences given by Kraus. We obtain for each order conditions for matrix…
Our study focuses on fractional order compartment models derived from underlying physical stochastic processes, providing a more physically grounded approach compared to models that use the dynamical system approach by simply replacing…
We consider general convolutional derivatives and related fractional statistical dynamics of continuous interacting particle systems. We apply the subordination principle to construct kinetic fractional statistical dynamics in the continuum…
This paper is devoted to the general theory of systems of time-fractional differential-operator equations. The representation formulas for solutions of systems of ordinary differential equations with single (commensurate) fractional order…
In this article a theoretical framework for problems involving fractional equations of hyperbolic type arising in the theory of viscoelasticity is presented. Based on the Galerkin method, a variational problem of the fractionary…
The following document presents some novel numerical methods valid for one and several variables, which using the fractional derivative, allow to find solutions for some non-linear systems in the complex space using real initial conditions.…
We study fractional variational problems of Herglotz type of variable order. Necessary optimality conditions, described by fractional differential equations depending on a combined Caputo fractional derivative of variable order, are proved.…
We present a comparative numerical study for three functionals used for variational mesh adaptation. One of them is a generalisation of Winslow's variable diffusion functional while the others are based on equidistribution and alignment.…
The variational discrete element method developed in [28] for dynamic elasto-plastic computations is adapted to compute the deformation of elastic Cosserat materials. In addition to cellwise displacement degrees of freedom (dofs), cellwise…
Unidirectional start-up flow of a viscoelastic fluid in a pipe with fractional Maxwell's model is studied. The flow starting from rest is driven by a constant pressure gradient in an infinite long straight pipe. By employing the method of…
We use an off-lattice discretization of fractional Brownian motion and a Metropolis Algorithm to determine the asymptotic scaling of this discretized fractional Brownian motion under the influence of an excluded volume as in the Edwards and…
We introduce a fractional calculus on time scales using the theory of delta (or nabla) dynamic equations. The basic notions of fractional order integral and fractional order derivative on an arbitrary time scale are proposed, using the…