Related papers: Quantitative Approximation Properties for the Frac…
Fractional differential equations provide a tractable mathematical framework to describe anomalous behavior in complex physical systems, yet they introduce new sensitive model parameters, i.e. derivative orders, in addition to model…
For the fractional diffusion-wave equation with the Caputo-Dzhrbashyan fractional derivative of order $\alpha \in (1,2)$ with respect to the time variable, we prove an analog of the principle of limiting amplitude (well-known for the wave…
We study the properties of a stochastic heat equation with a generalized mixed fractional Brownian noise. We obtain the covariance structure, stationarity and obtain bounds for the asymptotic behaviour of the solution. We suggest estimators…
We analyze a reaction coefficient identification problem for the spectral fractional powers of a symmetric, coercive, linear, elliptic, second-order operator in a bounded domain $\Omega$. We realize fractional diffusion as the…
In this manuscript we proposed a new fractional derivative with non-local and no-singular kernel. We presented some useful properties of the new derivative and applied it to solve the fractional heat transfer model.
We study here a heat-type differential equation of order n greater than two, in the case where the time-derivative is supposed to be fractional. The corresponding solution can be described as the transition function of a pseudoprocess…
We consider a class of nonlocal conservation laws with an interaction kernel supported on the negative real half-line and featuring a decreasing jump at the origin. We provide, for the first time, an existence and uniqueness theory for said…
In this paper, we prove a sample-path comparison principle for the nonlinear stochastic fractional heat equation on $\mathbb{R}$ with measure-valued initial data. We give quantitative estimates about how close to zero the solution can be.…
We survey methods and results of fractional differential equations in which an unknown function is under the operation of integration and/or differentiation of fractional order. As an illustrative example, we review results on fractional…
We discuss several new results on nonnegative approximate controllability for the one-dimensional Heat equation governed by either multiplicative or nonnegative additive control, acting within a proper subset of the space domain at every…
We introduce an efficient variational hybrid quantum-classical algorithm designed for solving Caputo time-fractional partial differential equations. Our method employs an iterable cost function incorporating a linear combination of overlap…
We investigate a fractional notion of gradient and divergence operator. We generalize the div-curl estimate by Coifman-Lions-Meyer-Semmes to fractional div-curl quantities, obtaining, in particular, a nonlocal version of Wente's lemma. We…
Fractional differential operators provide an attractive mathematical tool to model effects with limited regularity properties. Particular examples are image processing and phase field models in which jumps across lower dimensional subsets…
We consider a class of homogeneous partial differential operators on a finite-dimensional vector space and study their associated heat kernels. The heat kernels for this general class of operators are seen to arise naturally as the limiting…
We study the well-posedness of a semilinear fractional diffusion equation and formulate an associated inverse problem. We determine fractional power type nonlinearities from the exterior partial measurements of the Dirichlet-to-Neumann map.…
In this paper we study the influence of the Hardy potential in the fractional heat equation. In particular, we consider the problem $$(P_\theta)\quad \left\{ \begin{array}{rcl} u_t+(-\Delta)^{s} u&=&\l\dfrac{\,u}{|x|^{2s}}+\theta u^p+ c…
In this work, we obtain the numerical temperature field to a thermally developing fluid flow inside parallel plates problem with a quantum computing method. The physical problem deals with the heat transfer of a steady state,…
In this paper, we investigate stochastic heat equation with sublinear diffusion coefficients. By assuming certain concavity of the diffusion coefficient, we establish non-trivial moment upper bounds and almost sure spatial asymptotic…
In this paper, we study an adaptive finite element method for a class of a nonlinear eigenvalue problems that may be of nonconvex energy functional and consider its applications to quantum chemistry. We prove the convergence of adaptive…
For the kinetic energy of 1d model finite systems the leading corrections to local approximations as a functional of the potential are derived using semiclassical methods. The corrections are simple, non-local functionals of the potential.…