Abstract
In this paper, we take variable separation method to study Klein–Kramers (KK) equation. By choosing different eigenvalues and noise functions, we can get different probability density functions (PDFs) of KK equation. These PDFs contain not only normal distributions but also other distributions that correspond to anomalous diffusion phenomena. For example, power-law distribution, truncated Cauchy–Lorentz distribution, Weibull distribution, log-logistic distribution, Gamma distribution. We also show the 3D and 2D profiles of these PDFs to analyze the corresponding dynamic properties and illustrate the possible practical applications of these results. In addition, we also find some exact solutions that are not PDFs. They are also listed to ensure the completeness of the results and to illustrate the potential applications of these exact solutions.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
