INEQUALITIES GENERATED WITH RIEMANN-LIOUVILLE FRACTIONAL INTEGRAL OPERATOR

M. GURBUZ1, O. OZTURK2

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Abstract

The primary objective of this study is to handle new generalized midpoint, trapezoid and Simpson's type inequalities with the help of Riemann-Liouville fractional integral operator. In order to do this, a new fractional integral identity is obtained. Then by using this identity, some inequalities for the class of functions whose derivatives in absolute values at certain powers are convex are derived. It is observed that the obtained inequalities are generalizations of some results exist in the literature.

Keywords

Riemann-Liouville fractional integrals, Hadamard type inequalities, Simpson's inequality, convex functions.