An investigation of a closed-form solution for non-linear variable-order fractional evolution equations via the fractional Caputo derivative - Ali, Umair; Naeem, Muhammad; Alahmadi, Reham; Abdullah, Farah Aini; Khan, Muhammad Asim; Ganie, Abdul Hamid (Frontiers in Physics, 2023)
The nonlinear traveling or soliton wave solutions for variable-order fractional evolution equations (VO-FEE) is very challenging and important task in recent research fields. The aims of this study is to discuss the nonlinear space-time variable-order fractional shallow water wave equation that represent non-linear dispersive waves in the shallow water channel by Khater method in Caputo fractional derivative (CFD) sense. The transformation equation can be used to get the nonlinear integer-order ordinary differential equation (ODE) from the proposed equation. Also, built new exact solutions as Kink and periodic types solutions for nonlinear space-time variable-order fractional shallow water waves equation. This confirms the nonlinear fractional variable-order evolution equations are natural and very attractive in mathematical physics.