Inequalities of Simpson-Mercer-type including Atangana-Baleanu fractional operators and their applications

AIMS Mathematics

article

Muhammad Tariq¹  Hijaz Ahmad²  Soubhagya Kumar Sahoo³  Artion Kashuri⁴  Taher A. Nofal⁵  Ching-Hsien Hsu⁶ 

[1] Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology;Section of Mathematics, International Telematic University Uninettuno;Department of Mathematics, Department of Mathematics, Institute of Technical Education and Research, Siksha 'O' Anusandhan University;Department of Mathematics, Faculty of Technical and Natural Sciences, University Ismail Qemali;Department of Mathematics, College of Science, Taif University;Department of Computer Science and Information Engineering, Asia University;Department of Medical Research, China Medical University Hospital, China Medical University;Guangdong-Hong Kong-Macao Joint Laboratory for Intelligent Micro-Nano Optoelectronic Technology, School of Mathematics and Big Data, Foshan University

关键词: Jensen-Mercer inequality;    Simpson's inequality;    $ s $-convex functions;    Atangana-Baleanu fractional operator;    Hölder's inequalities;    q-digamma functions;    Modified Bessel functions;   

DOI  :  10.3934/math.2022831

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

Fractional operators with integral inequalities have attracted the interest of several mathematicians. Fractional inequalities are best utilized in mathematical science with their features and wide range of applications in optimization, modeling, engineering and artificial intelligence. In this article, we consider new variants of Simpson-Mercer type inequalities involving the Atangana-Baleanu (A-B) fractional integral operator for $ s $-convex functions. First, an integral identity, which acts as an auxiliary result for the main results is proved in the frame of fractional operator. Employing this new identity, some estimations of Simpson-Mercer type for $ s $-convex functions in the second sense are discussed. In addition, we study various new applications on Modified Bessel functions, special means and $ q $-digamma functions. These applications confirm the effectiveness and validity of the results and also bring a different dimension to the study.

【 授权许可】

CC BY