Hermite–Hadamard inequality for fractional integrals of Caputo–Fabrizio type and related inequalities

Journal of inequalities and applications

article

Mustafa Gürbüz¹  Ahmet Ocak Akdemir²  Saima Rashid³  Erhan Set⁴ 

[1] Department of Mathematics, Faculty of Education, Ağrı İbrahim Çeçen University;Department of Mathematics, Faculty of Arts and Sciences, Ağrı İbrahim Çeçen University;Department of Mathematics, Government College University;Department of Mathematics, Faculty of Arts and Sciences, Ordu University

关键词: Caputo–Fabrizio Fractional integral;    Convexity;   

DOI  :  10.1186/s13660-020-02438-1

学科分类：电力

来源: SpringerOpen

【 摘 要 】

In this article, firstly, Hermite–Hadamard’s inequality is generalized via a fractional integral operator associated with the Caputo–Fabrizio fractional derivative. Then a new kernel is obtained and a new theorem valid for convex functions is proved for fractional order integrals. Also, some applications of our main findings are given.

【 授权许可】

CC BY