Convexity in Terms of Caputo Fractional Derivatives

Abstract

The first criterion of convexity states that a differentiable function defined on an open interval is convex if and only if its first derivative is increasing. The second criterion of convexity states that a twice differential function is convex if and only if its second derivative is positive. In this work, by using a change of variable transforming the interval [𝑎, 𝑡] into [0, 1], we are able to get a new formulation of Caputo derivative.