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In this paper, we consider forward and inverse problems for subdiffusion equations with time-dependent coefficients. The fractional derivative is taken in the sense of Riemann-Liouville. Using the classical Fourier method, the theorem of…
One dimensional Stefan problems for a semi-infinite material with temperature dependent thermal coefficients are considered. Existence and uniqueness of solution are obtained imposing a Dirichlet or a Robin type condition at fixed face…
A novel constructive mathematical model based on the multifractal formalism in order to accurately characterizing the localized fluctuations present in the course of traffic flows today high-speed computer networks is presented. The…
In this contribution tracking control designs using output feedback are presented for a two-phase Stefan problem arising in the modeling of the Vertical Gradient Freeze process. The two-phase Stefan problem, consisting of two coupled free…
We report on generic relations between fractional flow and pressure in steady two-phase flow in porous media. The main result is a differential equation for fractional flow as a function of phase saturation. We infer this result from two…
In this work, we investigate entropy solutions for a class of systems of nonlocal {balance laws in which the convective flux and the source involves terms where the state variable convolved with kernels} in both spatial and temporal…
We study a class of one-dimensional interacting particle systems with random boundaries as a microscopic model for Stefan's melting and freezing problem. We prove that under diffusive rescaling these particle systems exhibit a hydrodynamic…
We complete the Solomon-Wilson-Alexiades's mushy zone model (Letters Heat Mass Transfer, 9 (1982), 319-324) for the one-phase Lam\'e-Clapeyron-Stefan problem. We obtain explicit solutions when a convective or heat flux boundary condition is…
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…
In this work, we investigate the estimation of the transient mold-slab heat flux in continuous casting molds given some thermocouples measurements in the mold plates. Mathematically, we can see this problem as the estimation of a Neumann…
We consider fractional diffusion equations and study the stability of the inverse problem of determining the time-dependent parameter in a source term or a coefficient of zero-th order term from observations of the solution at one point in…
In this work, we consider a number of boundary-value problems for time-fractional heat equation with the recently introduced Caputo-Fabrizio derivative. Using the method of separation of variables, we prove a unique solvability of the…
We assume that the Stefan problem with undercooling has a classical solution until the moment of contact of free boundaries and the free boundaries have finite velocities until the contact. Under these assumptions, we construct a smooth…
A mathematical model describing the flow of two-phase fluids in a bounded container $\Omega$ is considered under the assumption that the phase transition process is influenced by inertial effects. The model couples a variant of the…
We study a generalized version of the Gross-Neveu model in 2+1 dimensions. The model is inspired from Graphene, which shows a linear dispersion relation near the Dirac points. The phase structure and the thermodynamic properties in the mean…
Based on a recent work on traveling waves in spatially nonlocal reaction-diffusion equations, we investigate the existence of traveling fronts in reaction-diffusion equations with a memory term. We will explain how such memory terms can…
The Vlasov equation embodies the smooth field approximation of the self-consistent equation of motion for charged particle beams. This framework is fundamentally altered if we include the fluctuating forces that originate from the actual…
Many physical, biological, and engineered systems exhibit memory effects that challenge Markovian models. Fractional calculus provides nonlocal operators to capture hereditary dynamics. This survey connects modeling, analysis, and…
The solution of a Caputo time fractional diffusion equation of order $0<\alpha<1$ is expressed in terms of the solution of a corresponding integer order diffusion equation. We demonstrate a linear time mapping between these solutions that…
The behaviour of the solutions of the time-fractional diffusion equation, based on the Caputo derivative, is studied and its dependence on the fractional exponent is analysed. The time-fractional convection-diffusion equation is also solved…