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The group classification of a class of time fractional generalized KdV equations with variable coefficient is presented. The Lie symmetry analysis method is extended to the certain subclasses of time fractional generalized KdV equations with initial and boundary values. Under the corresponding similarity transformation with similarity invariants, KdV equations with initial and boundary values have been transformed into fractional ordinary differential equations with initial value. Then we use the power series method to obtain the exact solution of the reduced equation with the Erdélyi-Kober fractional differential operator.