A three-dimensional fractional solution for air contaminants dispersal in the planetary boundary layer

Alain Sylvain Tankou Tagne; Patrice Ele Abiama; Jean Marie Ema'a Ema'a; Pierre Owono Ateba; Germain Hubert Ben-Bolie

doi:10.1016/j.heliyon.2021.e07005

A three-dimensional fractional solution for air contaminants dispersal in the planetary boundary layer

Heliyon. 2021 May 26;7(5):e07005. doi: 10.1016/j.heliyon.2021.e07005. eCollection 2021 May.

Authors

Alain Sylvain Tankou Tagne¹, Patrice Ele Abiama¹, Jean Marie Ema'a Ema'a², Pierre Owono Ateba¹, Germain Hubert Ben-Bolie¹

Affiliations

¹ Laboratory of Nuclear Physics, Department of Physics, Faculty of Science, University of Yaounde I, PO Box 812, Yaounde, Cameroon.
² University of Maroua, Higher Teachers' Training College, PO Box 45, Maroua, Cameroon.

Abstract

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.

Keywords: Air contaminants modeling; Closed-form analytical solution; Fractional advection-diffusion equation.