On Some Inequalities Involving Liouville–Caputo Fractional Derivatives and Applications to Special Means of Real Numbers

Bessem Samet and Hassen Aydi
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Bessem Samet: Nonlinear Analysis Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam
Hassen Aydi: Department of Mathematics, College of Education in Jubail, Imam Abdulrahman Bin Faisal University, P.O. Box 12020, Jubail 31961, Saudi Arabia

Mathematics, 2018, vol. 6, issue 10, 1-9

Abstract: We are concerned with the class of functions f ∈ C 1 ( [ a , b ] ; R ) , a , b ∈ R , a < b , such that c D a α f is convex or c D b α f is convex, where 0 < α < 1 , c D a α f is the left-side Liouville–Caputo fractional derivative of order α of f and c D b α f is the right-side Liouville–Caputo fractional derivative of order α of f . Some extensions of Dragomir–Agarwal inequality to this class of functions are obtained. A parallel development is made for the class of functions f ∈ C 1 ( [ a , b ] ; R ) such that c D a α f is concave or c D b α f is concave. Next, an application to special means of real numbers is provided.

Keywords: Liouville–Caputo fractional derivative; convexity; Dragomir–Agarwal inequality (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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