Related papers: Inverse problem for the abstract diffusion-wave eq…
We consider the inverse problem of identification of degenerate diffusion coefficient of the form $x^\alpha a(x)$ in a one dimensional parabolic equation by some extra data. We first prove by energy methods the uniqueness and Lipschitz…
This article is concerned with an inverse problem of simultaneously determining a spatially varying coefficient and a Robin coefficient for a one-dimensional fractional diffusion equation with a time-fractional derivative of order…
We introduce a class of fractional Dirac type operators with time variable coefficients by means of a Witt basis, the Djrbashian-Caputo fractional derivative and the fractional Laplacian, both operators defined with respect to some given…
We study some inverse problems for time-fractional Schr\"odinger equations involving the Caputo derivative of fractional order $\alpha \in (0,1)$. We prove refined uniqueness results from sets of positive Lebesgue measure for various…
In the present paper we study inverse problems related to determining the time-dependent coefficient and unknown source function of fractional heat equations. Our approach shows that having just one set of data at an observation point…
We investigate the exact enlarged controllability and optimal control of a fractional diffusion equation in Caputo sense. This is done through a new definition of enlarged controllability that allows us to extend available contributions.…
We consider initial boundary value problems of time-fractional advection-diffusion equations with the zero Dirichlet boundary value $\partial_t^{\alpha} u(x,t) = -Au(x,t)$, where $-A = \sum}{i,j=1}^d \partial_i(a_{ij}(x)\partial_j) +…
In this paper, we investigate a nonlinear inverse problem aimed at recovering a coefficient $a(t, x)$, dependent on both time and a subset of spatial variables, in a diffusion equation \( u_t - \Delta_x u - u_{yy} +a(t, x) u = f(t,x,y) \),…
Inverse problem to determine simultaneously a general space- and time-dependent source and an initial state in a fractional diffusion equation from an {\it a posteriori} measurement of the normal derivative of the state on a portion of a…
This paper addresses the inverse scattering problem of a random potential associated with the polyharmonic wave equation in two and three dimensions. The random potential is represented as a centered complex-valued generalized microlocally…
Problems of calculus of variations with variable endpoints cannot be solved without transversality conditions. Here, we establish such type of conditions for fractional variational problems with the Caputo derivative. We consider: the…
The aim of this paper is to study time-fractional pseudo-parabolic type equations generated by the Dunkl operator. The forward problem is considered and its well-posedness is established. In particular, a prior estimates are obtained in the…
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 article, the Cauchy problem for the Langevin-type time-fractional equation $D_t^\beta(D_t^\alpha u(t))+D_t^\beta(Au(t))=f(t),(0<t\leq T)$ is studied. Here $\alpha,\beta \in(0,1)$, $D_t^\alpha, D_t^\beta$ is the Caputo derivative and…
This article proves the uniqueness for two kinds of inverse problems of identifying fractional orders in diffusion equations with multiple time-fractional derivatives by pointwise observation. By means of eigenfunction expansion and Laplace…
This article is devoted to the simultaneous resolution of three inverse problems, among the most important formulation of inverse problems for partial differential equations, stated for some class of diffusion equations from a single…
In this paper, we investigate a fractional differential equation involving sequential Caputo derivatives, motivated by recent research on fractional models with multiple memory effects. Using techniques inspired by earlier works on…
This paper is concerned with an inverse source problem for the stochastic wave equation driven by a fractional Brownian motion. Given the random source, the direct problem is to study the solution of the stochastic wave equation. The…
We consider a discretization of Caputo derivatives resulted from deconvolving a scheme for the corresponding Volterra integral. Properties of this discretization, including signs of the coefficients, comparison principles, and stability of…
We deal with the Cauchy problem for the space-time fractional diffusion-wave equation, which is obtained from the standard diffusion equation by replacing the second-order space derivative with a Riesz-Feller derivative of order alpha in…