On Conformable Double Laplace Transform and One Dimensional Fractional Coupled Burgers' Equation

In the present work we introduced a new method and name it the conformable double Laplace decomposition method to solve one dimensional regular and singular conformable functional Burger’s equation. We studied the existence condition for the conformable double Laplace transform. In order to obtain the exact solution for nonlinear fractional problems, then we modified the double Laplace transform and combined it with the Adomian decomposition method. Later, we applied the new method to solve regular and singular conformable fractional coupled Burgers’ equations. Further, in order to illustrate the effectiveness of present method, we provide some examples.

[1]  Mostafa Eslami,et al.  Exact traveling wave solutions to the fractional coupled nonlinear Schrodinger equations , 2016, Appl. Math. Comput..

[2]  Necati Özdemir,et al.  Optimal Control Problem for a Conformable Fractional Heat Conduction Equation , 2017 .

[3]  Ali Kurt,et al.  On conformable double Laplace transform , 2018 .

[4]  H. Bateman,et al.  SOME RECENT RESEARCHES ON THE MOTION OF FLUIDS , 1915 .

[5]  Thabet Abdeljawad,et al.  Conformable Fractional Semigroups of Operators , 2014, 1502.06014.

[6]  Cheng Chen,et al.  Simplest equation method for some time-fractional partial differential equations with conformable derivative , 2018, Comput. Math. Appl..

[7]  Jincun Liu,et al.  Numerical solutions of the space- and time-fractional coupled Burgers equations by generalized differential transform method , 2011, Appl. Math. Comput..

[8]  Thabet Abdeljawad,et al.  On conformable fractional calculus , 2015, J. Comput. Appl. Math..

[9]  Wei Zhao,et al.  A new definition of fractional derivative , 2019, International Journal of Non-Linear Mechanics.

[10]  J. Burgers.  A mathematical model illustrating the theory of turbulence , 1948 .

[11]  M. S. Hashemi,et al.  Invariant subspaces admitted by fractional differential equations with conformable derivatives , 2018 .

[12]  Hayman Thabet,et al.  Analytical solutions for conformable space-time fractional partial differential equations via fractional differential transform , 2018 .

[13]  Dumitru Baleanu,et al.  New exact solutions of Burgers’ type equations with conformable derivative , 2017 .

[14]  Jinqiao Duan,et al.  Limit set of trajectories of the coupled viscous Burgers' equations , 1996, Applied Mathematics Letters.

[15]  A. Kılıçman,et al.  A note on a singular coupled Burgers equation and double Laplace transform method , 2018 .