### Symmetry solution on fractional equation

#### Abstract

As we know nearly all physical, chemical, and biological processes in nature can be described or modeled by dint of a differential equation or a system of differential equations, an integral equation or an integro-differential equation. The differential equations can be ordinary or partial, linear or nonlinear. So, we concentrate our attention in problem that can be presented in terms of a differential equation with fractional derivative. Our research in this work is to use symmetry transformation method and its analysis to search exact solutions to nonlinear fractional partial differential equations.

#### Full Text:

PDF#### References

Diethelm, K. (2010). The analysis of fractional differential equations.Springer, Berlin.

Miller, K.S., Ross, B. (1993). An introduction to the fractional calculus and fractional differential equations. Wiley, New York.

Zelenyi, L.M., Milovanov, A.V. (2004). Fractal topology and strange kinetics: from percolation theory to problems in cosmic electrodynamics. Physics Uspekhi, 47, 749–788.

Bulut, H., Yel, G., Baskonus, H.M. (2016). An application of improved Bernoulli sub-equation function method to the nonlinear time-fractional Burgers equation. Turkish Journal of Mathematics and Computer Science, 5, 1–17.

Tarasov, V.E. (2006). Gravitational fi of fractal distribution of particles. Celes. Mech. Dynam. Astron., 19, 1–15.

Kaya, D., Bulut, H. (2000). The decomposition method for approximate solution of a burgers equation. Bulletin of the Institute of Mathematics Academia Sinica, 28, 35–42.

Wu, G., Lee, E.W.M. (2010) Fractional variational iteration method and its application. Phys. Lett. A., 374, 2506–2509.

Kaya, D., Bulut, H. (2000). On a comparison between decomposition method and one-step methods for nonlinear initial-value problems. Journal of natural and engineering sciences, 12(2), 299–305.

Barley, R., Torvik, P. (1983). A theoretical basis for the application of fractional calculus to viscoelasticity. J. Rheol., 27, 201–210.

Hereman, W., Banerjee, P.P., Chatterjee, M.R. (1989). On the nonlocal equations and nonlocal charges associated with the Harry-Dym hierarchy Korteweg-de-Vries equation. J. Phys. A., 22, 241–252.

Taghizadeh, N., Mirzazadeh, M., Rahimian, M., Akbari, M. (2013). Application of the simplest equation method to some time-fractional partial diff tial equations. Ain Shams Eng. J., 4(4), 897–902.

Baskonus, H.M., Mekkaoui, T., Hammouch, Z., Bulut, H. (2015) Active control of a chaotic fractional order economic system. Entropy, 17(8), 5771–5783.

Hu, J., Ye, Y., Shen, S., Zhang, J. (2014). Lie symmetry analysis of the time fractional dV-type equation. Appl. Math. and Comp., 223, 439–444.

Sahadevan, R., Bakkyaraj, T. (2012). Invariant analysis of time fractional generalized Burgers and Kortewegde Vries equations. J. Math. Anal. Appl., 393, 341–347.

Bluman, G.W., Anco, S. (2002). Symmetry and integration methods for differential equations. (Springer-Verlag, Heidelburg.

Gazizov, R.K., Kasatkin, A.A., Lukashchuk, S.Y. (2007). Continuous transformation group of fractional diff tial equations. Vestn. USATU, 9, 125-135.

DOI: http://dx.doi.org/10.11121/ijocta.01.2017.00498

### Refbacks

- There are currently no refbacks.

Copyright (c) 2017 Gulistan Iskandarova

This work is licensed under a Creative Commons Attribution 4.0 International License.