In this section, we give the description of the auxiliary equation method for solving fractional

partial differential equations.

Nuseir, "Symbolic methods to construct exact solutions of nonlinear

partial differential equations," Mathematics and Computers in Simulation, vol.

In the above given references, it could be seen that the investigation of exact solutions of nonlinear

partial differential equations played a significant role in the study of physical phenomena of nonlinear problems.

Dhaigude, Linear initial value problems for fractional

partial differential equations, Bull.

Manafian, "The solution of the variable coefficients fourth-order parabolic

partial differential equations by homotopy perturbation method," Zeitschrift fur Naturforschung, vol.

Now, we derive the leading order term [U.sub.0] and the correction term [U.sub.1] in a

partial differential equation form.

In this section we give the description of the Jacobi elliptic equation method for solving fractional

partial differential equations.

Russel: A unified boundary controllability theory for hyperbolic and parabolic

partial differential equations, Studies in Appl.

Partial differential equations (PDEs) played a vital role in natural sciences and engineering.

We now present the multiplier method for the derivation of conservation laws for

partial differential equations. We will outline its application to the

partial differential equation (1) in two independent variables.

Partial Differential Equations and Solitary Waves Theory Higher Education Press Beijing (2009).

These nonlinear

partial differential equations have no general solution, and only a limited number of exact solutions have been found in (Labropulu, 2000) and (Hamdan, 1998) [1-3].