Exact solutions for time-fractional Fokker-Planck-Kolmogorov equation of Geometric Brownian motion via Lie point symmetries

被引：6

作者：

Naderifard, Azadeh ^{[1
]}

Dastranj, Elham ^{[1
]}

Hejazi, S. Reza ^{[1
]}

机构：

[1] Shahrood Univ Technol, Fac Math Sci, Shahrood, Semnan, Iran

来源：

INTERNATIONAL JOURNAL OF FINANCIAL ENGINEERING | 2018年 / 5卷 / 02期

关键词：

Fokker-Planck equation; time-fractional PDE; geometric Brownian motion; lie symmetry;

D O I：

10.1142/S2424786318500093

中图分类号：

F8 [财政、金融];

学科分类号：

0202 ;

摘要：

In this paper, the transition joint probability density function of the solution of geometric Brownian motion (GBM) equation is obtained via Lie group theory of differential equations (DEs). Lie symmetry analysis is applied to find new solutions for time-fractional Fokker-Planck-Kolmogorov equation of GBM. This analysis classifies the forms of the solutions for the equation by the similarity variables arising from the symmetry operators. Finally, an analytic method called invariant subspace method is applied in order to find another exact solution.

引用

页数：15

共 50 条

[41] Stochastic dynamics from the fractional Fokker-Planck-Kolmogorov equation: Large-scale behavior of the turbulent transport coefficient
Milovanov, AV
[J]. PHYSICAL REVIEW E, 2001, 63 (04):
[42] Numerical solution for the time-fractional Fokker–Planck equation via shifted Chebyshev polynomials of the fourth kind
Haile Habenom
D. L. Suthar
[J]. Advances in Difference Equations, 2020
[43] Lie symmetry analysis and some new exact solutions of the Fokker-Planck equation
Al-Nassar, Samar
Nadjafikhah, Mehdi
[J]. ARABIAN JOURNAL OF MATHEMATICS, 2023, 12 (03) : 467 - 482
[44] EXACT-SOLUTIONS OF THE FOKKER PLANCK KOLMOGOROV EQUATION FOR CERTAIN MULTIDIMENSIONAL DYNAMIC-SYSTEMS
DIMENTBERG, MF
[J]. PMM JOURNAL OF APPLIED MATHEMATICS AND MECHANICS, 1983, 47 (04): : 458 - 460
[45] Symmetries, conservation laws and exact solutions of the time-fractional diffusivity equation via Riemann-Liouville and Caputo derivatives
Hejazi, S. Reza
Rashidi, Saeede
[J]. WAVES IN RANDOM AND COMPLEX MEDIA, 2019, 31 (04) : 690 - 711
[46] Exact solutions of a time-fractional modified KdV equation via bifurcation analysis
Liu, Min-Yuan
Xu, Hui
Wang, Zeng-Gui
[J]. CHINESE PHYSICS B, 2023, 32 (12)
[47] Exact solutions of a time-fractional modified KdV equation via bifurcation analysis
刘敏远
许慧
王增桂
[J]. Chinese Physics B, 2023, 32 (12) : 224 - 231
[48] Time-fractional Davey-Stewartson equation: Lie point symmetries, similarity reductions, conservation laws and traveling wave solutions
Guo, Baoyong
Fang, Yong
Dong, Huanhe
[J]. COMMUNICATIONS IN THEORETICAL PHYSICS, 2023, 75 (10)
[49] Anisotropic non-linear time-fractional diffusion equation with a source term: Classification via Lie point symmetries, analytic solutions and numerical simulation
Hejazi, S. Reza
Saberi, Elaheh
Mohammadizadeh, Fatemeh
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2021, 391
[50] New semi-analytical solutions of the time-fractional Fokker-Planck equation by the neural network method
Wei, Jia-Li
Wu, Guo-Cheng
Liu, Bao-Qing
Zhao, Zhengang
[J]. OPTIK, 2022, 259

← 1 2 3 4 5 →