The present work investigates the applicability and effectiveness of the generalized Riemann-Liouville fractional integral operator integral method to obtain new Minkowski, Grüss type and several other associated dynamic variants on an arbitrary time scale, which are communicated as a combination of delta and fractional integrals. These inequalities extend some dynamic variants on time scales, and tie together and expand some integral inequalities. The present method is efficient, reliable, and it can be used as an alternative to establishing new solutions for different types of fractional differential equations applied in mathematical physics.

本工作研究了广义Riemann-Liouville分数阶积分算子积分方法在任意时间尺度上获得新的Minkowski，Grüss类型和其他几个相关的动态变量的实用性和有效性，这些变量作为增量积分和分数积分的组合进行通信。这些不等式扩展了时间尺度上的一些动态变体，并将它们联系在一起并扩展了一些积分不等式。本方法是有效，可靠的，并且可以用作为数学物理中应用的不同类型的分数阶微分方程建立新解的替代方法。