分数阶反向累加与累减生成算子及互逆性

Mutual Invertibility of Fractional Order Opposite Direction Accumulating Generation Operator and Reducing Generation Operator

采用反向累加与反向累减的信息处理方式，将一阶累加生成算子和一阶累减生成算子拓展至分数阶范围，给出了分数阶反向累加生成算子与分数阶反向累减生成算子的解析表达式，并证明了两者之间的互逆性，为建立基于分数阶反向累加的灰色预测模型和拓宽灰色预测模型的应用范围提供理论基础．

The way of information processing by opposite direction accumulation and reducing, had been extended to the first order accumulating generation operator and reducing generation operator to fractional order, giving the mathematical expression of fractional order opposite direction accumulating generation operator and reducing generation operator. Then proof the properties of mutual invertibility of fractional order opposite direction accumulating generation operator and reducing generation operator. Expanding the opposite direction accumulating generation operator and reducing generation operator would help develop fractional order opposite direction accumulating grey prediction model and widen the application fields of grey prediction model.