Exact solutions and numerical simulations of time-fractional Fokker-Plank equation for special stochastic process

نویسندگان
Hejazi, Reza ID 1
Hosseinpour, Soleiman ID 2
Dastranj, Elham ID 3
Naderifard, Azadeh ID 4

1 Faculty of mathematical sciences, Shahrood university of technology, Shahrood, Semnan, Iran.

2 Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Semnan, Iran.

3 Faculty of mathematical sciences, Shahrood university of technology, Shahrood, Semnan, Iran.

4 Faculty of mathematical sciences, Shahrood university of technology, Shahrood, Semnan, Iran.

doi
10.22034/cmde.2019.30717.1458
چکیده

‎In this paper, a type of time-fractional Fokker-Planck equation (FPE) of the OrnsteinUhlenbeck process is solved via Riemann-Liouville and Caputo derivatives. An analytical method based on symmetry operators is used for finding reduced form and exact solutions of the equation. A numerical simulation based on the M¨untz-Legendre polynomials is applied in order to find some approximated solutions of the equation.

کلیدواژه‌ها
Fokker-Plank equation, Riemann Liouville derivative, Caputo derivative, Lie point symmetry, M¨untz-Legendre polynomial