Related papers: The Calder\'on Problem For The Fractional Magnetic…

We consider a time-independent variable coefficients fractional porous medium equation and formulate an associated inverse problem. We determine both the conductivity and the absorption coefficient from exterior partial measurements of the…

We consider the inverse Calder\'on problem consisting of determining the conductivity inside a medium by electrical measurements on its surface. Ideally, these measurements determine the Dirichlet-to-Neumann map and, therefore, one usually…

We study an inverse problem for the fractional Schr\"odinger equation (FSE) with a local perturbation by a linear partial differential operator (PDO) of order smaller than the order of the fractional Laplacian. We show that one can uniquely…

We study the inverse problem of determining the coefficients of the fractional power of a general second order elliptic operator given in the exterior of an open subset of the Euclidean space. We show the problem can be reduced into…

We consider the restricted Dirichlet-to-Neumann map $\Lambda^{U,V}_{g,A,q}$ for the wave equation with magnetic potential $A$ and scalar potential $q$, on an admissible Lorentzian manifold $(M, g)$ of dimension $n \geq 3$ with boundary.…

In this paper, we solve the fractional anisotropic Calder\'on problem with external data in the Euclidean space, in dimensions two and higher, for smooth Riemannian metrics that agree with the Euclidean metric outside a compact set.…

We calculate the fractional integral and derivative of the potential $1/r$ for all values of the fractional order $-1< \alpha \leq 0$ and $\alpha\geq 0$. We show that the result has the same form for all values of $\alpha$. Applications can…

Fractional calculus has been used to describe physical systems with complexity. Here, we show that a fractional calculus approach can restore or include complexity in any physical systems that can be described by partial differential…

Fractional derivatives and integrations of non-integers orders was introduced more than three centuries ago but only recently gained more attention due to its application on nonlocal phenomenas. In this context, several formulations of…

We study the Calder\'on problem for a logarithmic Schr\"odinger type operator of the form $L_{\Delta} +q$, where $L_{\Delta}$ denotes the logarithmic Laplacian, which arises as formal derivative $\frac{d}{ds} \big|_{s=0}(-\Delta)^s$ of the…

The paper deals with existence and multiplicity of solutions of the fractional Schr\"{o}dinger--Kirchhoff equation involving an external magnetic potential. As a consequence, the results can be applied to the special case \begin{equation*}…

This paper studies fractional integral operator for vector fields in weighted $L^1$. Using the estimates on fractional integral operator and Stein-Weiss inequalities, we can give a new proof for a class of Caffarelli-Kohn-Nirenberg…

Problems of the numerical solution of the Cauchy problem for a first-order differential-operator equation are discussed. A fundamental feature of the problem under study is that the equation includes a fractional power of the self-adjoint…

We consider fractional powers of non-densely defined non-negative operators in Banach spaces defined by means of the Balakrishnan operator. Under mild assumptions on the operator we show that the fractional powers can partially be obtained…

In this paper, we use the fractional calculus to discuss the fractional mechanics, where the time derivative is replaced with the fractional derivative of order $\nu$. We deal with the motion of a body in a resisting medium where the…

We introduce three types of partial fractional operators of variable order. An integration by parts formula for partial fractional integrals of variable order and an extension of Green's theorem are proved. These results allow us to obtain…

A fractional variational principle was derived in order to be used with lagrangians containing fractional derivatives of order 1/2. By forcing the action associated to this type of lagrangian to be stationary, a modified fractional…

We prove a unique continuation property for the fractional Laplacian $(-\Delta)^s$ when $s \in (-n/2,\infty)\setminus \mathbb{Z}$. In addition, we study Poincar\'e-type inequalities for the operator $(-\Delta)^s$ when $s\geq 0$. We apply…

In this paper we study inverse boundary value problems with partial data for the bi-harmonic operator with first order perturbation. We consider two types of subsets of $\mathbb{R}^{n}(n\geq 3)$, one is an infinite slab, the other is a…

We obtain a characterization of the weighted inequalities for the Riesz transforms on weighted local Morrey spaces. The condition is sufficient for the boundedness on the same spaces of all Calder\'on-Zygmund operators suitably defined on…