New Exact Solutions and Conservation Laws to the Fractional-Order Fokker-Planck Equations - Kadkhoda, Nematollah; Lashkarian, Elham; İnç, Mustafa; Akinlar, Mehmet Ali; Chu, Yu-Ming (Mdpi, 2020)
The main purpose of this paper is to present a new approach to achieving analytical solutions of parameter containing fractional-order differential equations. Using the nonlinear self-adjoint notion, approximate solutions, conservation laws and symmetries of these equations are also obtained via a new formulation of an improved form of the Noether's theorem. It is indicated that invariant solutions, reduced equations, perturbed or unperturbed symmetries and conservation laws can be obtained by applying a nonlinear self-adjoint notion. The method is applied to the time fractional-order Fokker-Planck equation. We obtained new results in a highly efficient and elegant manner.
Keywords: lie point symmetry analysis; approximate conservation laws; approximate nonlinear self-adjointness; perturbed fractional differential equations