Application of two different algorithms to the approximate long water wave equation with conformable fractional derivative

Abstract

The current paper devoted on two different methods to find the exact solutions with various forms including hyperbolic, trigonometric, rational and exponential functions of fractional differential equations systems with conformable farctional derivative. We have employed the modified simple equation and exp(Φ(ξ)) method here for the approximate long water wave equation. We have adopted here the fractional complex transform accompanied by properties of conformable fractional calculus for reduction of fractional partial differential equation systems to ordinary differential equation systems.