TY - JOUR
T1 - The closed-form solution by the exponential rational function method for the nonlinear variable-order fractional differential equations
AU - ALBaidani, Mashael M.
AU - Ali, Umair
AU - Ganie, Abdul Hamid
N1 - Publisher Copyright:
Copyright © 2024 ALBaidani, Ali and Ganie.
PY - 2024
Y1 - 2024
N2 - 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.
AB - 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.
KW - closed-form traveling wave solution
KW - exponential rational function method
KW - variable-order Caputo derivative
KW - variable-order fractional (2+1)-dimensional Burger hierarchy equation
KW - variable-order fractional modified Kawahara equation
UR - http://www.scopus.com/inward/record.url?scp=85200256398&partnerID=8YFLogxK
U2 - 10.3389/fphy.2024.1347636
DO - 10.3389/fphy.2024.1347636
M3 - Article
AN - SCOPUS:85200256398
SN - 2296-424X
VL - 12
JO - Frontiers in Physics
JF - Frontiers in Physics
M1 - 1347636
ER -