New Version of Fractional Pachpatte-Type Integral Inequalities via Coordinated ℏ-Convexity via Left and Right Order Relation

Abstract

In particular, the fractional forms of Hermite–Hadamard inequalities for the newly defined class of convex mappings proposed that are known as coordinated left and right ℏ-convexity (LR-ℏ-convexity) over interval-valued codomain. We exploit the use of double Riemann–Liouville fractional integral to derive the major results of the research. We also examine the key results’ numerical validations that examples are nontrivial. By taking the product of two left and right coordinated ℏ-convexity, some new versions of fractional integral inequalities are also obtained. Moreover, some new and classical exceptional cases are also discussed by taking some restrictions on endpoint functions of interval-valued functions that can be seen as applications of these new outcomes.

Keywords

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