Abstract
In this work, new [Formula: see text]-dimensional Korteweg–de Vries (KdV) equation and modified KdV (mKdV) equation as well as the corresponding fractional forms are presented. These two equations are derived for the first time relying on the extended [Formula: see text]-dimensional zero curvature equation. In addition, symmetries and conservation laws are displayed. Meanwhile, one-soliton solution for the time fractional of [Formula: see text]-dimensional KdV equation and mKdV equation is obtained.
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