New Exact Solutions and Conservation Laws to the Fractional-Order Fokker-Planck Equations
SYMMETRY-BASEL, vol.12, no.8, 2020 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 12 Issue: 8
- Publication Date: 2020
- Doi Number: 10.3390/sym12081282
- Journal Name: SYMMETRY-BASEL
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
- Open Archive Collection: AVESIS Open Access Collection
- Yıldız Technical University Affiliated: Yes
Abstract
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.