Study and analysis of a two‐dimensional nonconservative fractional order aerosol transport equation

The shifted Legendre collocation method is used to solve the two-dimensional fractional order aerosol equation with initial and boundary conditions. The solution profile of the equation is presented graphically for different cases. The important feature of the article is graphical exhibitions of the effect of the size of the aerosol particles and also the temporal derivative on the solution profile. The salient feature of the article is the demonstration of lower variation of mass concentration with the change in time level in fractional order systems than that in integer order system. A drive has been taken towards the tabular and pictorial presentations of a comparison of the numerical solution of our proposed method with an analytical solution of an existing problem through error analysis which conforms super-linearly convergence rate of the proposed method to validate its efficiency and effectiveness.