Some Nonlinear Fractional PDEs Involving β-Derivative by Using Rational exp−Ωη-Expansion Method

Abstract EN

In this article, some new nonlinear fractional partial differential equations (PDEs) (the space-time fractional order Boussinesq equation; the space-time (2 + 1)-dimensional breaking soliton equations; and the space-time fractional order SRLW equation) have been considered, in which the treatment of these equations in the diverse applications are described.

Also, the fractional derivatives in the sense of β-derivative are defined.

Some fractional PDEs will convert to consider ordinary differential equations (ODEs) with the help of transformation β-derivative.

These equations are analyzed utilizing an integration scheme, namely, the rational exp−Ωη-expansion method.

Different kinds of traveling wave solutions such as solitary, topological, dark soliton, periodic, kink, and rational are obtained as a by product of this scheme.

Finally, the existence of the solutions for the constraint conditions is also shown.

The outcome indicates that some fractional PDEs are used as a growing finding in the engineering sciences, mathematical physics, and so on.