Nonlinear fractional differential equations provide suitable models to describe real-world phenomena and many fractional derivatives are varying with time and space.The present study considers the advanced and broad s...Nonlinear fractional differential equations provide suitable models to describe real-world phenomena and many fractional derivatives are varying with time and space.The present study considers the advanced and broad spectrum of the nonlinear(NL)variable-order fractional differential equation(VO-FDE)in sense of VO Caputo fractional derivative(CFD)to describe the physical models.The VO-FDE transforms into an ordinary differential equation(ODE)and then solving by the modified(G/G)-expansion method.For ac-curacy,the space-time VO fractional Korteweg-de Vries(KdV)equation is solved by the proposed method and obtained some new types of periodic wave,singular,and Kink exact solutions.The newly obtained solutions confirmed that the proposed method is well-ordered and capable implement to find a class of NL-VO equations.The VO non-integer performance of the solutions is studied broadly by using 2D and 3D graphical representation.The results revealed that the NL VO-FDEs are highly active,functional and convenient in explaining the problems in scientific physics.展开更多
文摘Nonlinear fractional differential equations provide suitable models to describe real-world phenomena and many fractional derivatives are varying with time and space.The present study considers the advanced and broad spectrum of the nonlinear(NL)variable-order fractional differential equation(VO-FDE)in sense of VO Caputo fractional derivative(CFD)to describe the physical models.The VO-FDE transforms into an ordinary differential equation(ODE)and then solving by the modified(G/G)-expansion method.For ac-curacy,the space-time VO fractional Korteweg-de Vries(KdV)equation is solved by the proposed method and obtained some new types of periodic wave,singular,and Kink exact solutions.The newly obtained solutions confirmed that the proposed method is well-ordered and capable implement to find a class of NL-VO equations.The VO non-integer performance of the solutions is studied broadly by using 2D and 3D graphical representation.The results revealed that the NL VO-FDEs are highly active,functional and convenient in explaining the problems in scientific physics.
