时空分数阶的广义b-方程组的精确解

Exact Solutions for the Generalized b-Family Equations with Fractional Time and Spatial Derivatives

在这篇文章中,我们考虑在Riemann−Liouville意义下的时空分数阶广义b-方程组的精确解。我们将通过拉普拉斯变换给出这个方程组带初值条件的解析解。此外,本文将通过一个辅助方程证明这个方程组具有相同的解析解。

In this paper, the generalized b-family equations with fractional time and spatial derivatives are considered. The fractional derivative is described in the Riemann−Liouville sense. We present the analytical solutions of the fractional equations with initial con- ditions by the Laplace transform of sequential fractional derivatives. Moreover, the generalized b-family equations with fractional time and spatial derivatives possess com- mon analytical solutions which are solved by considering a simple equation.