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We prove new Ostrowski-type α-conformable dynamic inequalities and its companion inequalities on time scales by using the integration-by-parts formula on time scales associated with two parameters for functions with bounded second delta derivatives. When α = 1 , we obtain some well-known time-scale inequalities due to Ostrowski. As particular cases, we obtain new continuous and discrete inequalities. [ABSTRACT FROM AUTHOR]

Our work is based on the multiple inequalities illustrated by Boudeliou and Khalaf in 2015. With the help of the Leibniz integral rule on time scales, we generalize a number of those inequalities to a general time scale. Besides that, in order to obtain some new inequalities as special cases, we also extend our inequalities to discrete, quantum, and continuous calculus. These inequalities may be of use in the analysis of some kinds of partial dynamic equations on time scales and their applications in environmental phenomena, physical and engineering sciences described by partial differential equations. [ABSTRACT FROM AUTHOR]

In the present manuscript, we prove some new extensions of the dynamic Ostrowski inequality and its companion inequalities on an arbitrary time scale by using two parameters for functions whose second delta derivatives are bounded. In addition to these generalizations, some integral and discrete inequalities are obtained as special cases of main results. [ABSTRACT FROM AUTHOR]