A New Methodology for the Solution of the Advection-Diffusion Equation in the Planetary Boundary Layer Using Conformable Derivative

Abstract

The objective of this work is to describe a methodological proposal for the development of a solution of the fractional two-dimensional diffusion-advection equation considering a non-homogeneous planetary boundary layer (PBL). The method ADMM (Advection-Diffusion Multilayer Method) is used, which provides a semi-analytical solution based on the discretization of the PBL in sublayers, and the advection-diffusion equation is solved by applying the Laplace transform technique, now including the novelty of the conformable derivatives. This procedure generates a new methodology called  -ADMM.