Analytical solution of the time fractional Fokker-Planck equation

• Autorzy: Sutradhar T. , Datta B. K. , Bera R. K.

Identyfikatory

DOI

10.2478/ijame-2014-0030

• Języki publikacji: EN

Abstrakty

EN

A nonperturbative approximate analytic solution is derived for the time fractional Fokker-Planck (F-P) equation by using Adomian’s Decomposition Method (ADM). The solution is expressed in terms of Mittag-Leffler function. The present method performs extremely well in terms of accuracy, efficiency and simplicity.

Słowa kluczowe

EN

Fokker-Planck equation; Adomian decomposition method; fractional calculus; fractional differential equation

PL

równanie Fokkera-Plancka; równania różniczkowe; mechanika stosowana

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mechanics and Engineering
• Rocznik: 2014
• Tom: Vol. 19, no. 2
• Strony: 435--440
• Opis fizyczny: Bibliogr. 23 poz.

Twórcy

autor

Sutradhar T.

• Ranaghat Debnath Institution Mission Road, Ranaghat, PIN – 741 201 Nadia, West Bengal, INDIA

autor

Datta B. K.

• Department of Mathematics, Chakdaha College Chakdaha, PIN – 741 222 Nadia, West Bengal, INDIA

autor

Bera R. K.

• Heritage Institute of Technology BK-301, Sector-II, Chowbaga Road Anandapur, Kolkata – 700 107, INDIA

Bibliografia

• [1] Abbaoui K. and Cherruault Y. (1994): Convergence of Adomian’s method applied to differential equations. - Computers Math. Applic., vol.28(5), pp.103-109.
• [2] Abbaoui K. and Cherruault Y. (1995): New ideas for proving convergence of decomposition methods. - Computers Math. Applic., vol.29(7), pp.103-108.
• [3] Adomian G. (1994): Solving Frontier Problems of Physics: The Decomposition Method. - Boston: Kluwer Academic Publishers.
• [4] Adomian G. and Rach R. (1993): Analytic solution of nonlinear boundary-value problems in several dimensions by decomposition. - Jr. Math. Anal. Appl., vol.173(1), pp.118-137.
• [5] Cherruault Y. (1989): Convergence of Adomian’s method. - Kybernetes, vol.18, pp.31-38.
• [6] Datta B.K. (1993): The approximate evaluation of certain integrals. - Computers and Mathematics with Applications, vol.25(7), pp.47-49.
• [7] Datta B.K. (2007): In analysis and estimation of stochastic physical and mechanical system. - UGC Minor Research Project No.F. PSW/061.
• [8] Glockle W.G. and Nonnenmacher T.F. (1991): Fractional integral operators and Fox functions in the theory of viscoelasticity. - Macromolecules, vol.24, pp.6426-6434.
• [9] Himoun N., Abbaoui K. and Cherruault Y. (1999): New results of convergence of Adomian’s method. - Kybernetes, vol.28(4-5), pp.423-429.
• [10] Jiang K. (2005): Multiplicity of nonlinear thermal convection in a spherical shell. - Phys. Rev. E., Stat Nonlinear Soft Matter Phys., vol.71, No.1 Pt 2.
• [11] Kaya D. (2006): The exact and numerical solitary-wave solutions for generalized modified Boussinesq equation. - Physics Letters A, vol.348(3-6), pp.244-250.
• [12] Miller K.S. and Ross B. (1993): An introduction to the fractional calculus and fractional differential equations. - New York: John Wiley and Sons Inc.
• [13] Ngarhasta N., Some B., Abbaoui K. and Cherruault Y. (2002): New numerical study of Adomian method applied to a diffusion model. - Kybernetes, vol.31(1), pp.61-75.
• [14] Odibat Z. and Momani S. (2007): Numerical solution of Fokker-Planck equation with space and time-fractional derivatives. - Phys. Lett. A, vol.369, pp.349-358.
• [15] Oksendal B. (2004): Stochastic Differential Equations. - Springer International.
• [16] Oldham K.B. and Spanier J. (1974): The Fractional Calculus. - New York and London: Academic Press.
• [17] Podlubny I. (1999): Fractional Differential Equations. - San Diego, California, USA: Academic Press.
• [18] Rida, S.Z. and Sherbiny H.M. (2008): On the solution of the fractional nonlinear Schrödinger equation. - Phys. Lett. A, vol.372(5), pp.553-558.
• [19] Saha R.S., Chaudhuri K.S. and Bera R.K. (2008): Application of modified decomposition method for the analytical solution of space fractional diffusion equation. - Applied Mathematics and Computation, vol.196(1), pp.294-302.
• [20] Shawagfeh N.T. (2002): Analytical approximate solutions for nonlinear fractional differential equations. - Appl. Math. And Comp., vol.131, pp.517-529.
• [21] Suarez L.E. and Shokooh A. (1997): An eigenvector expansion method for the solution of motion containing fractional derivatives. - Transaction ASME Journal of Applied Mechanics, vol.64(3), pp.629-635.
• [22] Sutradhar T. (2009): Nonperturbative analytical solution of the time fractional nonlinear Burger’s equation. - Indian Journal of Physics, vol.83(12), pp.1681-1690.
• [23] Wazwaz A.M. (2002): Partial Differential Equations. Methods and Applications. - Lisse, The Netherlands: A.A. Balkema Publishers.