# A New Numerical Technique for Solving Systems Of Nonlinear Fractional Partial Differential Equations

## Main Article Content

### 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.

## Article Details

### References

- G. Adomian, Nonlinear Stochastic Systems Theory and Applications to Physics, Kluwer Academic Publishers, Netherlands, (1989).
- 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.
- G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic Publishers, Boston, (1994).
- G. Adomian, Solutions of nonlinear P.D.E, Appl. Math. Lett., 11 (1998), 121-123.
- Y. Zhu, Q. Chang and S. Wu, A new algorithm for calculating Adomian polynomials, Appl. Math. Comp., 169 (2005), 402-416.
- K. Diethelm, The Analysis Fractional Differential Equations, Springer-Verlag Berlin Heidelberg (2010).
- I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, CA, (1999).
- 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.
- D. Kumar, J. Singh and S. Rathore, Sumudu Decomposition Method for Nonlinear Equations, Int. Math. For., 7 (2012), 515 - 521.
- 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.
- 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.
- K. S. Aboodh, The new integral transform ”Aboodh Transform” , Glob. J. Pure. App. Math., 9 (1) (2013), 35-43.
- 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.
- 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.
- 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.
- 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.
- 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.