Abstract
In this article, we prove several new fractional nabla Bennett-Leindler dynamic inequalities with the help of a simple consequence of Keller's chain rule, integration by parts, mean inequalities and Holder's inequality for the nabla fractional derivative on time scales. As a result of this, some new classical inequalities are obtained as special cases, and we extended our inequalities to discrete and continuous calculus. In addition, when alpha = 1, we shall obtain some well-known dynamic inequalities as special instances from our results. Symmetrical properties are critical in determining the best ways to solve inequalities.