  We study solutions of a class of higher order partial differential equations
in bounded domains. These partial differential equations appeared first time in
the papers of Allouba and Zheng \cite{allouba1}, Baeumer, Meerschaert and Nane
\cite{bmn-07}, Meerschaert, Nane and Vellaisamy \cite{MNV}, and Nane
\cite{nane-h}. We express the solutions by subordinating a killed Markov
process by a hitting time of a stable subordinator of index $0<\beta <1$, or by
the absolute value of a symmetric $\alpha$-stable process with $0<\alpha\leq
2$, independent of the Markov process. In some special cases we represent the
solutions by running composition of $k$ independent Brownian motions, called
$k$-iterated Brownian motion for an integer $k\geq 2$. We make use of a
connection between fractional-time diffusions and higher order partial
differential equations established first by Allouba and Zheng \cite{allouba1}
and later extended in several directions by Baeumer, Meerschaert and Nane
\cite{bmn-07}.
