A novel analysis of integral inequalities in the frame of fractional calculus

In this paper, we define and explore the new family of exponentially convex functions which are called exponentially s–convex functions. We attain the amazing examples and algebraic properties of this newly introduced function. In addition, we find a novel version of Hermite-Hadamard type inequality in the support of this newly introduced concept via the frame of classical and fractional calculus (non-conformable and Riemann-Liouville integrals operator). Furthermore, we investigate refinement of Hermite-Hadamard type inequality by using exponentially s–convex functions via fractional integraloperator. Finally, we elaborate some Ostrowski type inequalities in the frame of fractional calculus. These new results yield us some generalizations of the prior results.