Z. Naturforsch. 68a, 777 – 784 (2013)
Numerical Computation of Time-Fractional Fokker–Planck Equation Arising in Solid State Physics and Circuit Theory
Sunil Kumar
Department of Mathematics, National Institute of Technology, Jamshedpur, 801014, Jharkhand, India
Received May 10, 2013 / revised July 31, 2013 / published online October 30, 2013
Reprint requests to: S. K.; E-mail: skumar.math@nitjsr.ac.in
The main aim of the present work is to propose a new and simple algorithm to obtain a quick and accurate analytical solution of the time fractional Fokker–Plank equation which arises in various fields in natural science, including solid-state physics, quantum optics, chemical physics, theoretical biology, and circuit theory. This new and simple algorithm is an innovative adjustment in Laplace transform algorithm which makes the calculations much simpler and applicable to several practical problems in science and engineering. The proposed scheme finds the solutions without any discretization or restrictive assumptions and is free from round-off errors and therefore reduces the numerical computations to a great extent. Furthermore, several numerical examples are presented to illustrate the accuracy and the stability of the method.
Key words: Fokker–Plank Equation; Mittag–Leffler Function; Analytical Solution; Homotopy Perturbation Method; Laplace Transform Method.
Full-text PDF