Abstract
In this paper, we study integral inequalities which will provide refinements of bounds of unified integral operators established for convex and α , m -convex functions. A new definition of function, namely, strongly α , m -convex function is applied in different forms and an extended Mittag-Leffler function is utilized to get the required results. Moreover, the obtained results in special cases give refinements of fractional integral inequalities published in this decade.
Highlights
Fractional integral operators are very useful and are extensively utilized in mathematics, physics, engineering, and many other subjects
Many classical inequalities have been studied for fractional integral operators of different kinds
We give some definitions of generalized fractional integral operators
Summary
Fractional integral operators are very useful and are extensively utilized in mathematics, physics, engineering, and many other subjects. The researchers have introduced variety of fractional integral operators, most of them generalize classical Riemann-Liouville integrals. In recent study of mathematical inequalities, fractional integral operators are playing an important role. Many classical inequalities have been studied for fractional integral operators of different kinds. One can see recent articles dealing with fractional inequalities in [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15] and in the references therein. We give some definitions of generalized fractional integral operators
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