Existence and Continuation of Solutions of Hilfer-Katugampola-Type Fractional Differential Equations

Approximate and mean approximate controllability properties for Hilfer time-fractional differential equations

We study the approximate and mean approximate controllability properties of fractional partial differential equations associated with the so-called Hilfer type time-fractional derivative and a non-negative selfadjoint operator $A_B$ with a compact resolvent on $L^2(Ω)$, where $Ω\subset\mathbb{R}^N$ ($N\ge 1$) is a bounded open set. More precisely, we show that if $0\leν\le 1$, $0<μ\le 1$ and $Ω\subset\mathbb R^N$ is a bounded open set, then the system $$\mathbb D_t^{μ,ν} u+A_Bu=f|_ω\;\; \mbox{ in }\; Ω\times (0,T),\,\, (\mathbb I_t^{(1-ν)(1-μ)}u)(\cdot,0)=u_0 \mbox{ in }\;Ω,$$ is approximately…