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In this study, we investigated some closed-form solutions for solving atmospheric dispersion issues under variable atmospherical hypothesis, in a vertically positioned non-homogeneous planetary boundary-layer. In our context, a nonidentical expansion for the solution of the fractional advection-diffusion equation in a non-integer dimensional-space was examined. In a nutshell, a Sturm-Liouville eigenvalue problem with more reliable information concerning the initial value problem is discussed. The performance of the model was estimated by presenting numerical simulations against experimental data. Under these meteorological conditions, fractional-order models performed far better than those of the classical integer-order ones.