Title: A New Numerical Technique for Solving Systems Of Nonlinear Fractional Partial Differential Equations
Author(s): Mountassir Hamdi Cherif, Djelloul Ziane
Pages: 188-197
Cite as:
Mountassir Hamdi Cherif, Djelloul Ziane, A New Numerical Technique for Solving Systems Of Nonlinear Fractional Partial Differential Equations, Int. J. Anal. Appl., 15 (2) (2017), 188-197.

Abstract


In this paper, we apply an efficient method called the Aboodh decomposition method to solve systems of nonlinear fractional partial differential equations. This method is a combined form of Aboodh transform with Adomian decomposition method. The theoretical analysis of this investigated for systems of nonlinear fractional partial differential equations is calculated in the explicit form of a power series with easily computable terms. Some examples are given to shows that this method is very efficient and accurate. This method can be applied to solve others nonlinear systems problems.

Full Text: PDF

 

References


  1. G. Adomian, Nonlinear Stochastic Systems Theory and Applications to Physics, Kluwer Academic Publishers, Netherlands, (1989). Google Scholar

  2. G. Adomian and R. Rach, Equality of partial solutions in the decomposition method for linear or nonlinear partial differential equations, Comput. Math. Appl., 10 (1990), 9-12. Google Scholar

  3. G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic Publishers, Boston, (1994). Google Scholar

  4. G. Adomian, Solutions of nonlinear P.D.E, Appl. Math. Lett., 11 (1998), 121-123. Google Scholar

  5. Y. Zhu, Q. Chang and S. Wu, A new algorithm for calculating Adomian polynomials, Appl. Math. Comp., 169 (2005), 402–416. Google Scholar

  6. K. Diethelm, The Analysis Fractional Differential Equations, Springer-Verlag Berlin Heidelberg (2010). Google Scholar

  7. I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, CA, (1999). Google Scholar

  8. A. K. H. Sedeeg and M. M. A. Mahgoub, Comparison of New Integral Transform Aboodh Transform and Adomian Decomposition Method, Int. J. Math. And App., 4 (2–B) (2016), 127-135. Google Scholar

  9. D. Kumar, J. Singh and S. Rathore, Sumudu Decomposition Method for Nonlinear Equations, Int. Math. For., 7 (2012), 515 - 521. Google Scholar

  10. D. Ziane and M. Hamdi Cherif, Resolution of Nonlinear Partial Differential Equations by Elzaki Transform De- composition Method, J. Appr. Theor. App. Math., 5 (2015), 17-30. Google Scholar

  11. H. M. Baskonus, H. Bulut and Y. Pandir, The natural transform decomposition method for linear and nonlinear partial differential equations, Math. Engineer. Scie. Aerospace., 5 (1) (2014), 111-126. Google Scholar

  12. K. S. Aboodh, The new integral transform ”Aboodh Transform” , Glob. J. Pure. App. Math., 9 (1) (2013), 35-43. Google Scholar

  13. M. M. A. Mahgoub and A. K. H. Sedeeg , An Efficient Method for Solving Linear and Nonlinear System of Partial Differential Equations, British. J. Math. Comp. Sci., 20 (1) (2017), 1-10. Google Scholar

  14. J. Ahmad, Z. Bibi and K. Noor, Laplace decomposition method using He’s polynomial to Burgers equation, J. Scie. Arts., 2 (27) (2014), 131-138. Google Scholar

  15. M. M. A. Mahgoub and A. K. H. Sedeeg , A Comparative Study of Homotopy Perturbation Aboodh Transform Method and Homotopy Decomposition Method for Solving Nonlinear Fractional Partial Differential Equations, Int. J. Theor. App. Math., 2 (2) (2016), 45-51. Google Scholar

  16. R. I. Nuruddeen and K. S. Aboodh, Analytical Solution For Time-Fractional Diffusion Equation By Aboodh De- composition Method, Int. J. Math. And App., 5 (1–A) (2017), 115-122. Google Scholar

  17. R. I. Nuruddeen and A. M. Nass, Aboodh Decomposition Method and its Application in Solving Linear and Nonlinear Heat Equations, Europ. J. Adv. Eng. Tech., 3 (7) (2016), 34-37. Google Scholar