New Exact Solutions and Conservation Laws to the Fractional-Order Fokker-Planck Equations

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Kadkhoda N., Lashkarian E., İNÇ M., AKINLAR M. A., Chu Y.

SYMMETRY-BASEL, vol.12, no.8, 2020 (SCI-Expanded) identifier identifier

  • 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
  • Yıldız Technical University Affiliated: Yes


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.