  The present work is devoted to investigate anisotropic conformal
transformation of conic pseudo-Finsler surfaces $(M,F)$, that is, $
F(x,y)\longmapsto \overline{F}(x,y)=e^{\phi(x,y)}F(x,y)$, where the function
$\phi(x,y)$ depends on both position $x$ and direction $y$, contrary to the
ordinary (isotropic) conformal transformation which depends on position only.
If $F$ is a pseudo-Finsler metric, the above transformation does not yield
necessarily a pseudo-Finsler metric. Consequently, we find out necessary and
sufficient condition for a (conic) pseudo-Finsler surface $(M,F)$ to be
transformed to a (conic) pseudo-Finsler surface $(M,\overline{F})$ under the
transformation $\overline{F}=e^{\phi(x,y)}F$. In general dimension, it is
extremely difficult to find the anisotropic conformal change of the inverse
metric tensor in a tensorial form. However, by using the modified Berwald frame
on a Finsler surface, we obtain the change of the components of the inverse
metric tensor in a tensorial form. This progress enables us to study the
transformation of the Finslerian geometric objects and the geometric properties
associated with the transformed Finsler function $\overline{F}$. In contrast to
isotropic conformal transformation, we have a non-homothetic conformal factor
$\phi(x,y)$ that preserves the geodesic spray. Also, we find out some invariant
geometric objects under the anisotropic conformal change. Furthermore, we
investigate a sufficient condition for $\overline{F}$ to be dually flat or/and
projectively flat. Finally, we study some special cases of the conformal factor
$\phi(x,y)$. Various examples are provided whenever the situation needs.
