Fractional Inequalities for Exponentially s-Convex Functions on Time Scales - Georgiev, Svetlin G.; Darvish, Vahid (Journal of Advances in Applied & Computational Mathematics, 2024)
In this paper, we present new integral inequalities involving exponentially s-convex functions in the second sense on time scales. By utilizing the delta Riemann-Liouville fractional integral and the fractional Taylor formula, we establish upper bounds for functions that are n-times rd-continuously Δ-differentiable with exponentially s-convex properties. Our results provide novel insights into the theory of time scales, bridging the gap between discrete and continuous calculus. The application of fractional calculus on time scales is explored, and several well-known inequalities are employed to derive the main findings. These results have potential implications for further studies in fractional dynamic calculus and other related fields. AMS Subject Classification: 39A10, 39A11, 39A20.