Some modifications in conformable fractional integral inequalities

Abstract

Abstract The prevalence of the use of integral inequalities has dramatically influenced the evolution of mathematical analysis. The use of these useful tools leads to faster advances in the presentation of fractional calculus. This article investigates the Hermite–Hadamard integral inequalities via the notion of Ϝ -convexity. After that, we introduce the notion of $\digamma _{\mu}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Ϝ</mml:mi> <mml:mi>μ</mml:mi> </mml:msub> </mml:math> -convexity in the context of conformable operators. In view of this, we establish some Hermite–Hadamard integral inequalities (both trapezoidal and midpoint types) and some special case of those inequalities as well. Finally, we present some examples on special means of real numbers. Furthermore, we offer three plot illustrations to clarify the results.