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

Author

Listed:
  • Bessem Samet

    (Nonlinear Analysis Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam
    Faculty of Mathematics and Statistics, 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)

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.

Suggested Citation

  • Bessem Samet & Hassen Aydi, 2018. "On Some Inequalities Involving Liouville–Caputo Fractional Derivatives and Applications to Special Means of Real Numbers," Mathematics, MDPI, vol. 6(10), pages 1-9, October.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:10:p:193-:d:174178
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