Nonholonomic Frame for a Deformed $(\alpha,\beta )$-metric

Recently, in paper [14], we have introduced the following deformed $(\alpha, \beta)$-metric: $$ F_{\epsilon}(\alpha,\beta)=\frac{\beta^{2}+\alpha^{2}(a+1)}{\alpha}+\epsilon\beta where $\alpha=\sqrt{a_{ij}y^{i}y^{j}}$ is a Riemannian metric; $\beta=b_{i}y^{i}$ 1-form, $\left|\epsilon\right|<2\sqrt{a+1}$ real parameter and $a\in \left(\frac{1}{4},+\infty\right)$ positive scalar. The aim of this to find nonholonomic frame for important kind \beta)$-metric also investigate Frobenius norm Hessian generated by metric.