Coordination of Classical and Dynamic Inequalities Complying on Time Scales

Abstract

In this research article, we present extensions of some classical inequalities such as Schweitzer, Pólya–Szegö, Kantorovich and Greub–Rheinboldt inequalities of fractional calculus on time scales. To investigate generalizations of such types of classical inequalities, we use the time scales Riemann–Liouville type fractional integrals. We explore dynamic inequalities on delta calculus and their symmetric nabla versions. A time scale is an arbitrary nonempty closed subset of the real numbers. The theory of time scales is applied to combine results in one comprehensive form. The calculus of time scales unifies and extends continuous versions and their discrete and quantum analogues. By using the calculus of time scales, results are presented in more general form. This hybrid theory is also widely applied on dynamic inequalities.