Some integral inequalities in interval fractional calculus for left and right coordinated interval-valued functions

Integral inequalities play a crucial role in both theoretical and applied mathematics. Because of the relevance of these notions, we have discussed a new class of introduced generalized convex function called as coordinated left and right convex interval-valued function (coordinated LR -convex IVF) using the pseudo-order relation ($ {\le }_{p} $). On interval space, this order relation is defined. First, a pseudo-order relation is used to show Hermite-Hadamard type inequality (HH type inequality) for coordinated LR -convex IVF. Second for coordinated LR -convex IVF, Some HH type inequalities are also derived for the product of two coordinated LR -convex IVFs. Furthermore, we have demonstrated that our conclusions cover a broad range of new and well-known inequalities for coordinated LR -convex IVFs and their variant forms as special instances which are defined by Zhao et al. and Budak et al. Finally, we have shown that the inclusion relation "$ \supseteq $" confidents to the pseudo-order relation "$ {\le }_{p} $" for coordinated LR -convex IVFs. The concepts and methodologies presented in this study might serve as a springboard for additional research in this field, as well as a tool for investigating probability and optimization research, among other things.