Inequalities for α-fractional differentiable functions

被引：95
作者：
Chu, Yu-Ming [1 ]
Khan, Muhammad Adil [2 ]
Ali, Tahir [2 ]
Dragomir, Sever Silvestru [3 ]
机构：
[1] Huzhou Univ, Dept Math, Huzhou 313000, Peoples R China
[2] Univ Peshawar, Dept Math, Peshawar 25000, Pakistan
[3] Victoria Univ, Coll Engn & Sci, Melbourne, Vic 8001, Australia
来源：
JOURNAL OF INEQUALITIES AND APPLICATIONS | 2017年
基金：
中国国家自然科学基金;
关键词：
convex function; Hermite-Hadamard inequality; fractional derivative; fractional integral; special mean; trapezoidal formula; HADAMARD-TYPE INEQUALITIES; CONVEX; MAPPINGS;
D O I：
10.1186/s13660-017-1371-6
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this article, we present an identity and several Hermite-Hadamard type inequalities for conformable fractional integrals. As applications, we establish some inequalities for certain special means of two positive real numbers and give the error estimations for the trapezoidal formula.
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页数：12
相关论文
共 33 条
  • [1] On conformable fractional calculus
    Abdeljawad, Thabet
    [J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2015, 279 : 57 - 66
  • [2] Abu Hammad M., 2014, Int. J. Differ. Equ. Appl., V13, P177
  • [3] Anderson D. R., 2016, CONTRIBUTIONS MATH E
  • [4] [Anonymous], INT J PURE APPL MATH
  • [5] [Anonymous], 2016, Progress in Fractional Differentiation and Applications, DOI DOI 10.18576/pfda/020204
  • [6] [Anonymous], INEQUALITITES INFINI
  • [7] Hermite-Hadamard type inequalities for the m- and (α, m)-logarithmically convex functions
    Bai, Rui-Fang
    Qi, Feng
    Xi, Bo-Yan
    [J]. FILOMAT, 2013, 27 (01) : 1 - 7
  • [8] Properties of h-convex functions related to the Hermite-Hadamard-Fejer inequalities
    Bombardelli, Mea
    Varosanec, Sanja
    [J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2009, 58 (09) : 1869 - 1877
  • [9] On the Fractional Difference Equations of Order (2,q)
    Cheng, Jin-Fa
    Chu, Yu-Ming
    [J]. ABSTRACT AND APPLIED ANALYSIS, 2011,
  • [10] Fractional Difference Equations with Real Variable
    Cheng, Jin-Fa
    Chu, Yu-Ming
    [J]. ABSTRACT AND APPLIED ANALYSIS, 2012,
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