3 papers
math.AP2026
Direct and inverse abstract Cauchy problems with fractional powers of almost sectorial operators
Joel E. Restrepo
We derive the explicit solution operator of an abstract Cauchy problem involving a time-variable coefficient and a fractional power of an almost sectorial operator. The time-variab…
math.AP2025
Abstract Volterra integral equations of wave type with almost sectorial operators
Joel E. Restrepo
We study classical solutions (existence, uniqueness, and explicit solution operator) for homogeneous, linear, and semilinear abstract Volterra integral equations of wave type with…
math.AP2025
Anomaly of the fractional heat propagator in abstract settings
Joel E. Restrepo
We study the following time-fractional heat equation: \begin{equation*} ^{C}\partial_{t}^αu(t)+\mathscr{L}u(t)=0,\quad u(0)=u_0\in X, \quad t\in[0,T],\quad T>0,\quad 0<α<1, \end{…