4 papers · 1 filter
Reconstruction algorithms for the fractional Laplacian and applications to inverse problems
Ethan Rinaldo, Mahamadi Warma
We introduce two reconstruction schemes that enable the recovery of a function in the entire Euclidean space from local data , where is a…
A unified view of nonlinear, nonlocal operators and qualitative properties of associated elliptic and parabolic problems
Ralph Chill, Mahamadi Warma
We put together a general framework to deal with elliptic and parabolic equations associated with (nonlinear) nonlocal (fractional order) operators. Many well-known nonlocal operat…
Superdiffusive fractional dynamics: Unveiling regularity results in systems with general positive self-adjoint operators
Edgardo Alvarez, Ciprian G. Gal, Valentin Keyantuo +1
We investigate the following fractional order in time Cauchy problem \begin{equation*} \begin{cases} \mathbb{D}_{t}^{α}u(t)+Au(t)=f(u(t)), & 1<α<2, \\ u(0)=u_{0},\,\,\,u^{\prime…
Boundary observation and control for fractional heat and wave equations
Umberto Biccari, Mahamadi Warma, Enrique Zuazua
We establish boundary observability and control for the fractional heat equation over arbitrary time horizons , within the optimal range of fractional exponents $s \in (1/2,…