Analyzing Boole’s type Inequalities for General Convex Functions via Generalized Fractional Integrals with their Computational Analysis and Applications

Abstract

Fractional calculus extends the differentiation and integration of functions to non-integer order. This work presents a new identity to represent specific differentiable mappings through generalized fractional integrals. On the basis of the newly established identity, several Boole’s type inequalities for differentiable generalized convex functions are obtained. Generalized fractional integrals are more versatile as compared to the traditional integral operators because they embody them. This method brings the connection between integer order calculus and fractional calculus, which gives more effective tools for solving non-singular problems where integer order calculus tools can be ineffective. The results provide further understanding of geometric properties of differentiable mappings and generalized convex functions which give rise to new identities and inequalities enriching the field of integral inequalities. Some numerical examples and applications are given in order to support these results as more feasible and relevant.