The first integral method for some time fractional differential equations

Abstract

a b s t r a c tIn this paper, the fractional derivatives in the sense of modified Riemann-Liouville derivative and the first integral method are employed for constructing the exact solutions of nonlinear time-fractional partial differential equations. The power of this manageable method is presented by applying it to several examples. This approach can also be applied to other nonlinear fractional differential equations.

Modified Trial Equation Method to the Nonlinear Fractional Sharma–Tasso–Olever Equation

“…The solutions (17) and (21) obtained by using the modified trial equation method for Eq. (1) have been checked by Mathematica.…”

“…For a better understanding, we plot solutions (17), (21) and (32) of the nonlinear fractional Sharma-Tasso-Olever equation in Fig. 1-3, which shows the dynamics of solutions with suitable parametric choices.…”

“…In Section III, as an application, we solve the nonlinear fractional partial differential equation such as the time-fractional Sharma-Tasso-Olever equation [17], [18] …”

Exact Solutions for a Local Fractional DDE Associated with a Nonlinear Transmission Line

“…Though solving a fractional differential equation (FDE) is a quite difficult task, the theory of FDEs is furnished with some solution methods, theoretical and numerical. Among them are the differential transform method, [4] the Adomian decomposition method, [5] the finite element method, [6] the finite difference method, [7] the homotopy perturbation method, [8] the fractional subequation method, [9] the first integral method, [10] and so on. A good survey on numerical methods for FDEs can be found in Ref.…”

New Exact Solutions of the Time-Fractional Nonlinear Dispersive KdV Equation

“…The exact solutions of these problems, when they exist, are very important in the understanding of the nonlinear fractional physical phenomena. There are a lot of methods which can be constituted the wave solutions for some time fractional differential equations [4], [5]. Single kink soliton solutions, compacton-like solutions, singular solitons and other solutions have been found by use of these approaches.…”