论文标题
在拉瓜尔的分数差异化上
On the Laguerre fractional integro-differentiation
论文作者
论文摘要
讨论了laguerre衍生$（dxd）^α，\ d \ equiv {d \ of dx} $的分数解释。引入了相应的分数积分。介绍了映射和半群属性，积分表示和梅林变换分析。证明了与Riemann-Liouville分数积分的关系。最后，涉及拉瓜式分数积分的伏特拉型的第二种积分方程是根据双重高几何类型序列求解的。
A fractional power interpretation of the Laguerre derivative $(DxD)^α,\ D\equiv {d\over dx} $ is discussed. The corresponding fractional integrals are introduced. Mapping and semigroup properties, integral representations and Mellin transform analysis are presented. A relationship with the Riemann-Liouville fractional integrals is demonstrated. Finally, a second kind integral equation of the Volterra-type, involving the Laguerre fractional integral is solved in terms of the double hypergeometric type series as the resolvent kernel.
