Approximate Analytical Solutions to Conformable Modified Burgers Equation Using Homotopy Analysis Method
By:
References
- [1] Abdeljawad T., On conformable fractional calculus, J. Comput. Appl. Math. 279 (2015), 57–66.
- [2] Atangana A., Baleanu D., Alsaedi A., New properties of conformable derivative, Open Math. 13 (2015), 889–898.
- [3] Çenesiz Y., Baleanu D., Kurt A., Tasbozan O., New exact solutions of Burgers’ type equations with conformable derivative, Waves Random Complex Media 27 (2017), no. 1, 103–116.
- [4] Eslami M., Exact traveling wave solutions to the fractional coupled nonlinear Schrodinger equations, Appl. Math. Comput. 285 (2016), 141–148.
- [5] He S., Sun K., Mei X., Yan B., Xu S., Numerical analysis of a fractional-order chaotic system based on conformable fractional-order derivative, Eur. Phys. J. Plus 132 (2017), no. 1, Art. 36, 11 pp.
- [6] Khalil R., Al Horani M., Yousef A., Sababheh M., A new definition of fractional derivative, J. Comput. Appl. Math. 264 (2014), 65–70.
- [7] Kilbas A.A., Srivastava H.M., Trujillo J.J., Theory and Applications of Fractional Differential Equations, Elsevier Science, San Diego, 2006.
- [8] Kurt A., Çenesiz Y., Tasbozan O., On the solution of Burgers’ equation with the new fractional derivative, Open Phys. 13 (2015), 355–360.
- [9] Liao S.J., The proposed homotopy analysis technique for the solution of nonlinear problems, Ph.D. Thesis, Shanghai Jiao Tong University, Shanghai, 1992.
- [10] Liao S.J., Beyond Perturbation. Introduction to the Homotopy Analysis Method, Chapman & Hall/CRC, Boca Raton, 2004.
- [11] Liao S.J., Notes on the homotopy analysis method: some definitions and theorems, Commun. Nonlinear Sci. Numer. Simul. 14 (2009), no. 4, 983–997.10.1016/j.cnsns.2008.04.013
- [12] Miller K.S., Ross B., An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons, New York, 1993.
- [13] Nicolescu B.N., Macarie T., Petrescu T.C., Application of homotopy analysis method for solving equation of vehicle’s move in the linear case, Applied Mechanics and Materials 822 (2016), 3–11.
- [14] Oruç Ö., Bulut F., Esen A., A Haar wavelet-finite difference hybrid method for the numerical solution of the modified Burgers’ equation, J. Math. Chem. 53 (2015), no. 7, 1592–1607.
- [15] Podlubny I., Fractional Differential Equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, Academic Press, San Diego, 1999.
- [16] Tasbozan O., Kurt A., Approximate analytical solution of ZK-BBM equation, Sohag J. Math. 2 (2015), no. 2, 57–60.
- [17] Ünal E., Gökdo§an A., Solution of conformable fractional ordinary differential equations via differential transform method, Optik 128 (2017), 264–273.
Language: English
Page range: 159 - 167
Submitted on: Feb 7, 2018
Accepted on: Aug 25, 2018
Published on: Jul 18, 2019
Published by: University of Silesia in Katowice, Institute of Mathematics
In partnership with: Paradigm Publishing Services
Publication frequency: 2 times per year
Related subjects:
© 2019 Ali Kurt, Orkun Tasbozan, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.