  We consider different types of processes obtained by composing Brownian
motion $B(t)$, fractional Brownian motion $B_{H}(t)$ and Cauchy processes $%
C(t)$ in different manners.
  We study also multidimensional iterated processes in $\mathbb{R}^{d},$ like,
for example, $\left( B_{1}(|C(t)|),...,B_{d}(|C(t)|)\right) $ and $\left(
C_{1}(|C(t)|),...,C_{d}(|C(t)|)\right) ,$ deriving the corresponding partial
differential equations satisfied by their joint distribution.
  We show that many important partial differential equations, like wave
equation, equation of vibration of rods, higher-order heat equation, are
satisfied by the laws of the iterated processes considered in the work.
  Similarly we prove that some processes like $%
C(|B_{1}(|B_{2}(...|B_{n+1}(t)|...)|)|)$ are governed by fractional diffusion
equations.
