相关论文: Energy-dissipation for time-fractional phase-field…

We proceed to a critical examination of the method used in nuclear fragmentation to exhibit signals of negative heat capacity. We show that this method leads to unsatisfactory results when applied to a simple and well controlled model.…

This work is devoted to infinite-energy solutions of semi-linear wave equations in unbounded smooth domains of $\mathbb{R}^3$ with fractional damping of the form $(-\Delta_x+1)^\frac{1}{2}\partial_t u$. The work extends previously known…

This paper systematically treats the asymptotic behavior of many (linear/nonlinear) classes of higher-order fractional differential equations with multiple terms. To do this, we utilize the characteristics of Caputo fractional…

In the present work we consider the electromagnetic wave equation in terms of the fractional derivative of the Caputo type. The order of the derivative being considered is 0 <\gamma<1. A new parameter \sigma, is introduced which…

In this paper, we prove sharp blow-up and global existence results for a time fractional diffusion-wave equation with a nonlinear memory term in a bounded domain, where the fractional derivative in time is taken in the sense of Caputo type.…

In this paper we study some cases of time-fractional nonlinear dispersive equations (NDEs) involving Caputo derivatives, by means of the invariant subspace method. This method allows to find exact solutions to nonlinear time-fractional…

Phase-field approaches to fracture based on energy minimization principles have been rapidly gaining popularity in recent years, and are particularly well-suited for simulating crack initiation and growth in complex fracture networks. In…

We consider the time-fractional Cattaneo equation involving the tempered Caputo space-fractional derivative. We find the characteristic function of the related process and we explain the main differences with previous stochastic treatments…

We study the fractional gravity for spacetimes with non-integer dimensions. Our constructions are based on a geometric formalism with the fractional Caputo derivative and integral calculus adapted to nonolonomic distributions. This allows…

The strong maximum principle is a remarkable characterization of parabolic equations, which is expected to be partly inherited by fractional diffusion equations. Based on the corresponding weak maximum principle, in this paper we establish…

The Cahn--Hilliard equation is a widely used model that describes amongst others phase separation processes of binary mixtures or two-phase flows. In the recent years, different types of boundary conditions for the Cahn--Hilliard equation…

We briefly review our recent results on the geometry of nonholonomic manifolds and Lagrange--Finsler spaces and fractional calculus with Caputo derivatives. Such constructions are used for elaborating analogous models of fractional gravity…

Fractional diffusion and Fokker-Planck equations are widely used tools to describe anomalous diffusion in a large variety of complex systems. The equivalent formulations in terms of Caputo or Riemann-Liouville fractional derivatives can be…

This paper presents a new partial differential equation to build Brakke's motion, which is a weak notion of mean curvature flow. We call the equation a modified Allen-Cahn equation abbreviated to MAC. After that we introduce its benefit: An…

We propose a probabilistic construction for the solution of a general class of fractional high order heat-type equations in the one-dimensional case, by using a sequence of random walks in the complex plane with a suitable scaling. A time…

This paper presents a numerical method to solve a time-fractional Burgers equation, achieving order of convergence $(2-\alpha)$ in time, here $\alpha$ represents the order of the time derivative. The fractional derivative is modeled by…

The first part of this paper introduces sufficient conditions to determine conservation laws of diffusion equations of arbitrary fractional order in time. Numerical methods that satisfy a discrete analogue of these conditions have…

We examine the fractional derivative of composite functions and present a generalization of the product and chain rules for the Caputo fractional derivative. These results are especially important for physical and biological systems that…

This paper is about the fractional Schr\"odinger equation expressed in terms of the Caputo time-fractional and quantum Riesz-Feller space fractional derivatives for particle moving in a potential field. The cases of free particle (zero…

We prove that any given function can be smoothly approximated by functions lying in the kernel of a linear operator involving at least one fractional component. The setting in which we work is very general, since it takes into account…