F-Expansion Method and Its Application for Finding Exact Analytical
Solutions of Fractional order RLW Equation
Abstract
Exact nonlinear partial differential equation solutions are critical for
describing new complex characteristics in a variety of fields of applied
science. The aim of this research is to use the F-expansion method to
find the generalized solitary wave solution of the regularized long wave
(RLW) equation of fractional order. Fractional partial differential
equations can also be transformed into ordinary differential equations
using fractional complex transformation and the properties of the
modified Riemann–Liouville fractional-order operator. Because of the
chain rule and the derivative of composite functions, nonlinear
fractional differential equations (NLFDEs) can be converted to ordinary
differential equations. We have investigated various set of explicit
solutions with some free parameters using this approach. The solitary
wave solutions are derived from the moving wave solutions when the
parameters are set to special values. Our findings show that this
approach is a very active and straightforward way of formulating exact
solutions to nonlinear evolution equations that arise in mathematical
physics and engineering. It is anticipated that this research will
provide insight and knowledge into the implementation of novel methods
for solving wave equations.