Some New Estimations of Left and Right Interval Fractional Pachpatte’s Type Integral Inequalities via Rectangle Plane

Abstract

Inequalities involving fractional operators have been an active area of research, which is crucial in establishing bounds, estimates, and stability conditions for solutions to fractional integrals. In this paper, we initially presented a new class that is known as coordinated left and right ℏ-pre-invex interval-valued mappings (C·L·R-ℏ-pre-invex Ι·V-M), as well classical convex and nonconvex are also obtained. This newly defined class enabled us to derive novel inequalities, such as Hermite–Hadamard and Pachpatte’s type inequalities. Furthermore, the obtained results allowed us to recapture several special cases of known results for different parameter choices, which can be applications of the main results. Finally, we discussed the validity of the main outcomes.

Keywords

• interval-valued mappings over coordinates
• coordinated left and right ℏ-convexity
• double Riemann–Liouville fractional integral operator
• Pachpatte’s type inequalities