<p>The main aim of this research article is to introduce and analyze multidimensional generalized Laplace fractional derivatives of functions with values in sequentially complete locally convex spaces. We precisely compute the multidimensional Laplace transform for some classes of mixed partial fractional derivatives in a two-dimensional setting. We also investigate subordination principles for multidimensional vector-valued Laplace transform and some classes of abstract partial fractional differential inclusions with multidimensional generalized Laplace fractional derivatives.</p>