  We propose a generalisation of analytic in a domain function of bounded
index, which was introduced by J. G. Krishna and S. M. Shah \cite{krishna}. In
fact, analytic in the unit ball function of bounded index by Krishna and Shah
is an entire function. Our approach allows us to explore properties of analytic
in the unit ball functions.
  We proved the necessary and sufficient conditions of bounded $L$-index in
direction for analytic functions. As a result, they are applied to study
partial differential equations and get sufficient conditions of bounded
$L$-index in direction for analytic solutions. Finally, we estimated growth for
these functions.
