NUMERICAL SOLUTION OF TIME-FRACTIONAL ORDER FOKKER-PLANCK EQUATION

Volume: 9 Number: 3 September 1, 2019
  • A. Prakash
  • M. Kumar
EN

NUMERICAL SOLUTION OF TIME-FRACTIONAL ORDER FOKKER-PLANCK EQUATION

Abstract

In this article, new iterative method NIM is employed to nd the numerical solution of linear and nonlinear time-fractional order Fokker-Planck equation FPE , which is applied in many elds of engineering and applied science. The introduced technique renders an analytical solution in the form of a convergent series with easily computable components without using any restrictive assumptions. Three numerical examples are tested using this method. Plotted graph illustrate the eciency and accuracy of the proposed method.

Keywords

References

  1. He, J. H., (1997), Variational iteration method for delay differential equations, Commun. Nonlinear Sci. Numer. Simul., 2(4), pp. 235-236.
  2. He, J. H., (1998), Approximate solution of nonlinear differential equations with convolution product nonlinearities, Comput. Methods Appl. Mech. Engrg., 167, pp. 69-73.
  3. He, J. H., (1999), Variational iteration method a kind of non-linear analytical technique: some examples, Int. J. Nonlinear Mech., 34, pp. 699-708.
  4. Prakash, A., Kumar. M and Sharma, K. K., (2015), Numerical method for solving fractional coupled Burgers equations, Applied Mathematics and Computation, 260, pp. 314-320.
  5. Prakash, A. and Kumar. M., (2016), He’s Variational iteration method for the solution of nonlinear Newell-Whitehead-Segel equation, Journal of Applied Analysis and Computation, 6(3), pp. 738-748.
  6. Prakash, A. and Kumar, M., (2016), Numerical solution of two dimensional time fractional-order biological population model, Open Physics, 14, pp. 177186.
  7. Prakash, A. and Kumar, M., (2017), Numerical method for solving time fractional multi-dimensional diffusion equations, Int. J. Computing Science and Mathematics, 8(3), pp. 257-267.
  8. Aruna. K and Ravi Kanth, A. S. V., (2013), Approximate solutions of nonlinear fractional Schrodinger equation via differential transform method and modified differential transform method, National Academy Science Letters, 36(2), pp. 201-213

Details

Primary Language

English

Subjects

-

Journal Section

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Authors

A. Prakash This is me

M. Kumar This is me

Publication Date

September 1, 2019

Submission Date

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Acceptance Date

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Published in Issue

Year 2019 Volume: 9 Number: 3

APA
Prakash, A., & Kumar, M. (2019). NUMERICAL SOLUTION OF TIME-FRACTIONAL ORDER FOKKER-PLANCK EQUATION. TWMS Journal of Applied and Engineering Mathematics, 9(3), 446-454. https://izlik.org/JA76RM38HW
AMA
1.Prakash A, Kumar M. NUMERICAL SOLUTION OF TIME-FRACTIONAL ORDER FOKKER-PLANCK EQUATION. JAEM. 2019;9(3):446-454. https://izlik.org/JA76RM38HW
Chicago
Prakash, A., and M. Kumar. 2019. “NUMERICAL SOLUTION OF TIME-FRACTIONAL ORDER FOKKER-PLANCK EQUATION”. TWMS Journal of Applied and Engineering Mathematics 9 (3): 446-54. https://izlik.org/JA76RM38HW.
EndNote
Prakash A, Kumar M (September 1, 2019) NUMERICAL SOLUTION OF TIME-FRACTIONAL ORDER FOKKER-PLANCK EQUATION. TWMS Journal of Applied and Engineering Mathematics 9 3 446–454.
IEEE
[1]A. Prakash and M. Kumar, “NUMERICAL SOLUTION OF TIME-FRACTIONAL ORDER FOKKER-PLANCK EQUATION”, JAEM, vol. 9, no. 3, pp. 446–454, Sept. 2019, [Online]. Available: https://izlik.org/JA76RM38HW
ISNAD
Prakash, A. - Kumar, M. “NUMERICAL SOLUTION OF TIME-FRACTIONAL ORDER FOKKER-PLANCK EQUATION”. TWMS Journal of Applied and Engineering Mathematics 9/3 (September 1, 2019): 446-454. https://izlik.org/JA76RM38HW.
JAMA
1.Prakash A, Kumar M. NUMERICAL SOLUTION OF TIME-FRACTIONAL ORDER FOKKER-PLANCK EQUATION. JAEM. 2019;9:446–454.
MLA
Prakash, A., and M. Kumar. “NUMERICAL SOLUTION OF TIME-FRACTIONAL ORDER FOKKER-PLANCK EQUATION”. TWMS Journal of Applied and Engineering Mathematics, vol. 9, no. 3, Sept. 2019, pp. 446-54, https://izlik.org/JA76RM38HW.
Vancouver
1.A. Prakash, M. Kumar. NUMERICAL SOLUTION OF TIME-FRACTIONAL ORDER FOKKER-PLANCK EQUATION. JAEM [Internet]. 2019 Sep. 1;9(3):446-54. Available from: https://izlik.org/JA76RM38HW