Approximate Analytical Solutions to Conformable Modified Burgers Equation Using Homotopy Analysis Method

[1] Abdeljawad T., On conformable fractional calculus, J. Comput. Appl. Math. 279 (2015), 57–66.10.1016/j.cam.2014.10.016Search in Google Scholar

[2] Atangana A., Baleanu D., Alsaedi A., New properties of conformable derivative, Open Math. 13 (2015), 889–898.10.1515/math-2015-0081Search in Google Scholar

[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, 103–116.10.1080/17455030.2016.1205237Search in Google Scholar

[4] Eslami M., Exact traveling wave solutions to the fractional coupled nonlinear Schrodinger equations, Appl. Math. Comput. 285 (2016), 141–148.10.1016/j.amc.2016.03.032Search in Google Scholar

[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.10.1140/epjp/i2017-11306-3Search in Google Scholar

[6] Khalil R., Al Horani M., Yousef A., Sababheh M., A new definition of fractional derivative, J. Comput. Appl. Math. 264 (2014), 65–70.10.1016/j.cam.2014.01.002Search in Google Scholar

[7] Kilbas A.A., Srivastava H.M., Trujillo J.J., Theory and Applications of Fractional Differential Equations, Elsevier Science, San Diego, 2006.Search in Google Scholar

[8] Kurt A., Çenesiz Y., Tasbozan O., On the solution of Burgers’ equation with the new fractional derivative, Open Phys. 13 (2015), 355–360.10.1515/phys-2015-0045Search in Google Scholar

[9] Liao S.J., The proposed homotopy analysis technique for the solution of nonlinear problems, Ph.D. Thesis, Shanghai Jiao Tong University, Shanghai, 1992.Search in Google Scholar

[10] Liao S.J., Beyond Perturbation. Introduction to the Homotopy Analysis Method, Chapman & Hall/CRC, Boca Raton, 2004.10.1115/1.1818689Search in Google Scholar

[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.2008.04.013Open DOISearch in Google Scholar

[12] Miller K.S., Ross B., An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons, New York, 1993.Search in Google Scholar

[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), 3–11.10.4028/www.scientific.net/AMM.822.3Search in Google Scholar

[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, 1592–1607.10.1007/s10910-015-0507-5Search in Google Scholar

[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.Search in Google Scholar

[16] Tasbozan O., Kurt A., Approximate analytical solution of ZK-BBM equation, Sohag J. Math. 2 (2015), no. 2, 57–60.Search in Google Scholar

[17] Ünal E., Gökdo§an A., Solution of conformable fractional ordinary differential equations via differential transform method, Optik 128 (2017), 264–273.10.1016/j.ijleo.2016.10.031Search in Google Scholar