Approximate analytical solutions to conformable modified Burgers equation using homotopy analysis method
Abstract
In this paper the authors aspire to obtain the approximate analytical solution of Modified Burgers Equation with newly defined conformable derivative by employing homotopy analysis method (HAM).
Keywords
modified Burgers equation; conformable derivative; homotopy analysis method
References
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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.
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., Gökdoğan A., Solution of conformable fractional ordinary differential equations via differential transform method, Optik 128 (2017), 264–273.
KurtA., & TasbozanO. (2018). Approximate analytical solutions to conformable modified Burgers equation using homotopy analysis method. Annales Mathematicae Silesianae, 33, 159-167. Retrieved from https://www.journals.us.edu.pl/index.php/AMSIL/article/view/13666
Ali Kurt
Department of Mathematics, Faculty of Science and Art, Mustafa Kemal University, Turkey Turkey
Department of Mathematics, Faculty of Science and Art, Mustafa Kemal University, Turkey Turkey
Orkun Tasbozan
otasbozan@mku.edu.tr
Department of Mathematics, Faculty of Science and Art, Mustafa Kemal University, Turkey Turkey
Department of Mathematics, Faculty of Science and Art, Mustafa Kemal University, Turkey Turkey
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