Abstract
Three nonlinear fractional models, videlicet, the space-time fractional 1 + 1 Boussinesq equation, 2 + 1 -dimensional breaking soliton equations, and SRLW equation, are the important mathematical approaches to elucidate the gravitational water wave mechanics, the fractional quantum mechanics, the theoretical Huygens’ principle, the movement of turbulent flows, the ion osculate waves in plasma physics, the wave of leading fluid flow, etc. This paper is devoted to studying the dynamics of the traveling wave with fractional conformable nonlinear evaluation equations (NLEEs) arising in nonlinear wave mechanics. By utilizing the oncoming exp − Θ q -expansion technique, a series of novel exact solutions in terms of rational, periodic, and hyperbolic functions for the fractional cases are derived. These types of long-wave propagation phenomena played a dynamic role to interpret the water waves as well as mathematical physics. Here, the form of the accomplished solutions containing the hyperbolic, rational, and trigonometric functions is obtained. It is demonstrated that our proposed method is further efficient, general, succinct, powerful, and straightforward and can be asserted to install the new exact solutions of different kinds of fractional equations in engineering and nonlinear dynamics.
Highlights
The solutions of fractional partial differential equations (FPDEs) are often of interest and are applied in practical life
We will discuss the physical explanation of the found exact solutions to three nonlinear fractional models
These figures are dependent on the family conditions which are of importance physically
Summary
The solutions of fractional partial differential equations (FPDEs) are often of interest and are applied in practical life. In the past few decades, a lot of studies have been executed to find the new and further exact traveling wave solution of space-time fractional PDEs by many research. This work mainly investigates three nonlinear fractional models by utilizing the oncoming exp ð−ΘðqÞÞ-expansion method [17, 25]. [28], authors constructed an analytical solution for both linear and nonlinear time-fractional Boussinesq equations by an iterative method. Inc and coworkers presented the new soliton structures to some time-fractional nonlinear differential equations with a conformable derivative via the Ricatti–Bernoulli sub-ODE method [51].
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