Ostrowski type inequalities via exponentially $s$-convexity on time scales

We introduce the concept of exponentially $s$-convexity in second sense on a time scale interval. prove among other things that if $f: [a, b]\to \mathbb{R}$ is an $s$-convex function, then \begin{align*} &\frac{1}{b-a}\int_a^b f(t)\Delta t\\ &\leq \frac{f(a)}{e_{\beta}(a, x_0) (b-a)^{2s}}(h_2(a, b))^s+\frac{f(b)}{e_{\beta}(b, (b-a)^{2s}}(h_2(b, a))^s, \end{align*} where $\beta$ positively regressive function. By considering special cases our scale, one can derive loads interesting new inequalities. The results obtained herein are novel to best knowledge and they complement existing literature.