The closed-form solution by the exponential rational function method for the nonlinear variable-order fractional differential equations - ALBaidani, Mashael M.; Ali, Umair; Ganie, Abdul Hamid (Frontiers in Physics, 2024)
The symmetry features of fractional differential equations allow them to explain physical and biological phenomena in nature effectively. The generalized form of the fractional differential equations is the variable-order fractional differential equations that describe the physical and biological applications. This paper discusses the closed-form traveling wave solutions for the nonlinear space-time variable-order fractional modified Kawahara and (2+1)-dimension Burger hierarchy equations. The variable-order fractional differential equation has a derivative operator in the Caputo sense that is converted into the integer-order ordinary differential equation (ODE) by the fractional transformation. The obtained ODE is solved by the exponential rational function method and as a result, constructed new exact solutions. Two problems are given to confirm the solutions of the space-time variable-order fractional differential equations.