Abstract : In this study, we show how the conformable Elzaki transform Homotopy perturbation method (ETHPM) may be used to resolve the non-linear time-fractional equation of Fokker-planck. Four distinct varieties of non-linear time-fractional FPE are solved using the proposed method. Finally, a quick look at the numerical findings is taken at several different values of. The proposed strategy is both easy to implement and effective in practice.
Keywords : FPE, ETHPM, non-linear time factional, Brownian motion.
Cite : Lal, D., & Vir, K. (2024). Relevance Of The Ethpm To The Numerical Solution Of Nonlinear Space-Time Fractional Equation Of Fokker-Planck (1st ed., pp. 244-251). Noble Science Press. https://doi.org/10.52458/9788197112492.nsp.2024.eb.ch-25
References :
Dubey R.S., Alkahtani B.S.T, Atangana A. (2015): “Analytical solution of space-time fractional fokker-planck equation by homotopy perturbation sumudu transform method”, Article ID-780929, 7 pages
Firoozjaee M.A., Youse S.A., Jafari H. (2015): “A numerical approach to fokker-planck equation with space- and time-fractional and non fractional derivatives”, Communications in Mathematical and in Computer Chemistry, 74:449-464.
Garg M., Manohar P. (2011): “Analytical solution of space-time fractional fokker planck equations by generalized differential transform method”, LE MATEMATICHE, LXVI: 91-101.
Habenom H., Suthar D.L. (2020): “Numerical solution for the time-fractional Fokker–Planck equation via shifted Chebyshev polynomials of the fourth kind”, Advances in Difference Equations, 315:1-16.
Hemeda A.A., Eladdad E.E. (2018): “New iterative methods for solving fokker-planck equation”, Article ID-6462174, 9 pages
Iqbal S., Martinez F., Kaabar Md. K.A., S. Md. E. (2022): “A novel Elzaki transform homotopy perturbation method for solving time-fractional non-linear partial differential equations”, Boundary Value Problems, 91:1-23.
Jassim A.M. (2013): “He’s variational iteration method for space-time fractional Fokker-Plank equation”, Journal of college of Education for pure science, 3(1):11-21.
Lal D., Vir K. (2022): “Laplace transform and Homotopy perturbation method for nonlinear Fokker-Planck equations”, Journal of algebraic statistics, 13(2):2446-2457.
Magdziarz M. , Weron A. , Weron K. (2007): “Fractional Fokker-Planck dynamics: stochas- tic representation and computer simulation.” Physical Review E, 75:016708 (1-6).
Nuntadilok B. (2021): “The solution of some nonlinear space-time fractional Fokker-Planck equations by using homotopy perturbation method”, Journal of Physics: Conference Series, 1850 (012093):1-6.
Prakash A., Kaur H. (2017): “Numerical solution for fractional model of Fokker-Planck equation by using q-HATM”,Chaos, Solitons and Fractals, 15:99-110.
