AUTHOR=ALBaidani Mashael M. , Ali Umair , Ganie Abdul Hamid TITLE=The closed-form solution by the exponential rational function method for the nonlinear variable-order fractional differential equations JOURNAL=Frontiers in Physics VOLUME=12 YEAR=2024 URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2024.1347636 DOI=10.3389/fphy.2024.1347636 ISSN=2296-424X ABSTRACT=

The symmetry features of fractional differential equations allow effective explanation of physical and biological phenomena in nature. 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)-dimensional 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 fractional transformation. The obtained ODE is solved by the exponential rational function method, and as a result, new exact solutions are constructed. Two problems are proposed to confirm the solutions of the space-time variable-order fractional differential equations.