Travelling-wave solutions for some fractional partial differential equation by means of generalized trigonometry functions

Abstract

Making use of a Fan's sub-equation method and the Mittag-Leffler function with aid of the symbolic computation system Maple we construct a family of traveling wave solutions of the Burgers and the KdV equations. The obtained results include periodic, rational and solitonlike solutions.

On the numerical solutions of some fractional ordinary differential equations by fractional Adams-Bashforth-Moulton method

“…If we apply FABMM to (30) by taking 0 < t Ä 1, step size n D 300 and initial condition u.0/ D 0, we can obtain a numerical solution for (30) for the first ten term and error accounts. Next, to determine the accuracy of the technique, we use L 2 nodal norm defined by:…”

Fractional transformation method for constructing solitary wave solutions to some nonlinear fractional partial differential equations

“…Following the steps of applying the sine-cosine method to equation (24), the solutions of equation 22are…”

“…where u = u(t, X). Then, we use the wave variable z = X −cs which reduce the PDE of (33) into the same ODE as in (24) and (29). Therefore, the solutions of equation 32are…”

A Boiti-Leon Pimpinelli equations with time-conformable derivative

“…For constructing such solutions, there exist numerous efficient techniques. For example, Sumudu homotopy perturbation transform method [1]- [4], Lie symmetry method [5], tan(φ(ξ)/2)− expansion method [6,7], generalized trigonometry functions [8], Riccati equation expansion technique [9], Jacobi elliptic function technique [10] and extended Jacobian elliptic function technique [11], etc. For more informations about the analytical methods, we refer the reader to the following references [12]- [20].…”