Abstract
AbstractThe present paper applies the variation of(G^{\prime} /G)-expansion method on the space-time fractional Hirota–Satsuma coupled KdV equation with applications in physics. We employ the new approach to receive some closed form wave solutions for any nonlinear fractional ordinary differential equations. First, the fractional derivatives in this research are manifested in terms of Riemann–Liouville derivative. A complex fractional transformation is applied to transform the fractional-order ordinary and partial differential equation into the integer order ordinary differential equation. The reduced equations are then solved by the method. Some novel and more comprehensive solutions of these equations are successfully constructed. Besides, the intended approach is simplistic, conventional, and able to significantly reduce the size of computational work associated with other existing methods.
Highlights
The present paper applies the variation of (G′/G)-expansion method on the space-time fractional Hirota–Satsuma coupled KdV equation with applications in physics
We have manipulated the unique method for obtaining more general closed form wave structures of the nonlinear fractional differential equations (FDEs), such as the space-time fractional Hirota–Satsuma coupled KdV equation [36]. The improvement of this process over the existing rule is that it presents a few novel closed-form wave solutions
We investigate equation (6) through the transformation u = u(x, t) = u(ξ ), ξ = kxβ + λt β, where k and λ are nonzero arbitrary constants, equation (6) becomes
Summary
Abstract: The present paper applies the variation of (G′/G)-expansion method on the space-time fractional Hirota–Satsuma coupled KdV equation with applications in physics. We employ the new approach to receive some closed form wave solutions for any nonlinear fractional ordinary differential equations. It is an indispensable task to attain the closed-form wave structures of the fractional differential equations (FDEs). We have manipulated the unique method for obtaining more general closed form wave structures of the nonlinear FDEs, such as the space-time fractional Hirota–Satsuma coupled KdV equation [36]. The improvement of this process over the existing rule is that it presents a few novel closed-form wave solutions. Some notable characteristics for the fractional derivative are as follows:
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