1 research outputs found
Memory approximate controllability properties for higher order Hilfer time fractional evolution equations
In this paper we study the approximate controllability of fractional partial
differential equations associated with the so-called Hilfer type time
fractional derivative and a non-negative selfadjoint operator with a
compact resolvent on , where \Omega\subset\RR^N () is
an open set. More precisely, we show that if , and
\Omega\subset\RR^N is an open set, then the system \begin{equation*}
\begin{cases} \D^{\mu,\nu}_tu+Au=f\chi_{\omega}\;\;&\mbox{ in
}\;\Omega\times(0,T),\\ (I_t^{(1-\nu)(2-\mu)}u)(\cdot,0)=u_0 &\mbox{ in
}\;\Omega,\\ (\partial_tI_t^{(1-\nu)(2-\mu)}u)(\cdot,0)=u_1 &\mbox{ in
}\;\Omega, \end{cases} \end{equation*} is memory approximately controllable for
any , , and any non-empty open
set . The same result holds for every
and .Comment: arXiv admin note: text overlap with arXiv:2003.0818