Caputo Fractional Derivative Inequalities for modified \(h,m\)−Convex Functions

Fractional calculus has emerged as a powerful tool in various branches of science and engineering, including mathematical modeling of complex phenomena. In particular, the Caputo k-fractional derivative has been extensively used to model various real-world problems. In this paper, we focus on developing Hadamard type inequalities for modified (h,m)−convex functions via the Caputo k−fractional derivatives. The main objective of this paper is to provide a new approach to estimating the fractional derivative of modified (h,m)−convex functions through the use of two integral identities involving the nth order derivatives of given functions. The results obtained in this paper can have significant applications in various fields of engineering and physics, including the modeling of complex systems governed by fractional differential equations.