Uniformity of dynamic inequalities constituted on time Scales

Abstract

In this article, we present extensions of some well-known inequalities such as Young's inequality and Qi's inequality on fractional calculus of time scales. To find generalizations of such types of dynamic inequalities, we apply the time scale Riemann-Liouville type fractional integrals. We investigate dynamic inequalities on delta calculus and their symmetric nabla results. The theory of time scales is utilized to combine versions in one comprehensive form. The calculus of time scales unifies and extends some continuous forms and their discrete and quantum inequalities. By applying the calculus of time scales, results can be generated in more general form. This hybrid theory is also extensively practiced on dynamic inequalities.