FRACTIONAL INEQUALITIES OF MILNE-TYPE FOR TWICE DIFFERENTIABLE QUASI−CONVEX AND P− FUNCTIONS

Author(s) : SINAN ASLAN AND AHMET OCAK AKDEMIR

Abstract:

In this paper, a fundamental identity concerning twice differentiable functions is utilized as a key
analytical tool. Utilizing this identity in the context of Riemann–Liouville fractional integrals, we establish novel
Milne-type inequalities of fractional nature for functions whose second derivatives exhibit quasi-convexity and
satisfy the conditions of P− function class. The methodology further involves the application of classical Holder
and Young inequalities, leading to diverse and original results in the context of these generalized convexity
concepts. The outcomes presented in this study not only enrich the theoretical framework of quasi-convex and
P−functions but also contribute novel perspectives and techniques to the field of fractional calculus and integral
inequalities.