Main Article Content
In this paper, a combined form of natural transform with homotopy analysis method is proposed to solve nonlinear fractional partial differential equations. This method is called the fractional homotopy analysis natural transform method (FHANTM). The FHANTM can easily be applied to many problems and is capable of reducing the size of computational work. The fractional derivative is described in the Caputo sense. The results show that the FHANTM is an appropriate method for solving nonlinear fractional partial differentia equation.
- Z. H. Khan and W. A. Khan, N-transform properties and applications, NUST J. Eng. Sci, 1 (2008), 127-133.
- R. Silambarasn and F. B. M. Belgacem, Applications of the Natural Transform to Maxwell's Equations, Prog. Elect. Res. Symp. Proc. Suzhou. China, (2011), 899-902.
- S. K. Q. Al-Omari, On the Application of Natural Transforms, Int. J. Pure Appl. Math. 85 (2013), 729-744.
- M. Junaid, Application Of Natural Transform To Newtonian Fluid Problems, Int. J. Sci. Technol. 5 (2016), 138-147.
- D. Loonker and P. K. Banerji, Solution of Fractional Ordinary Differential Equations by Natural Transform, Int. J. Math. Eng. Sci. 2 (2013), 1-7.
- S.J. Liao, The proposed homotopy analysis technique for the solution of nonlinear problems, Ph.D. Thesis, Shanghai Jiao Tong University, 1992.
- S. J. Liao, Beyond Perturbation: Introduction to Homotopy Analysis Method, Chapman and Hall/CRC Press, Boca Raton, 2003.
- S. J. Liao, On the homotopy analysis method for nonlinear problems, Appl. Math. Comput. 147 (2004), 499-513.
- I. Podlubny, Fractional Differential Equations, Academic Press, New York, 1999.
- A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006.
- K. Diethelm, The Analysis Fractional Differential Equations, Springer-Verlag Berlin Heidelberg 2010.
- F. B. M. Belgacem and R. Silambarasn, Theory of natural transform, Math. Eng. Sci. Aerospace, 3 (2012), 105-135.
- D. Loonker and P.K. Banerji, Solution of Fractional Ordinary Differential Equations by Natural Transform, Int. J. Math. Eng. Sci. 2 (2013), 1-7.
- A. Wazwaz, The variational iteration method for rational solutions for KdV, K(2,2), Burgers, and cubic Boussinesq equations, J. Comput. Appl. Math, 207 (2007), 18-23.