On the Fractional Mean Value

Abstract

This work, dealt with the classical mean value theorem and took advantage of it in the fractional calculus. The concept of a fractional critical point is introduced. Some sufficient conditions for the existence of a critical point is studied and an illustrative example rele- vant to the concept of the time dilation effect is given. The present paper also includes, some connections between convexity (and monotonicity) with fractional derivative in the Riemann-Liouville sense.