New integral inequalities for differentiable convex functions via Atangana-Baleanu fractional integral operators. (February 2021)

• Record Type: Journal Article
• Authors: Set, Erhan; Butt, Saad Ihsan; Akdemir, Ahmet Ocak; Karaoǧlan, Ali; Abdeljawad, Thabet
• Is Part Of: Chaos, solitons and fractals. Volume 143(2021)
• Publication Date: 2021-02
• Subjects: Differentiable convex functions -- Hölder inequality -- Young inequality -- Power mean inequality -- Atangana-Baleanu fractional integral; 26A33 -- 26A51 -- 26D10; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2020.110554
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: Contain interesting results linking fractional analysis and inequality theory. Hadamard type results in inequality theory for the Atangana-Baleanu integral operator. New approaches and bounds for Hadamard-type inequalities. New and motivated inequalities derived from the help of Jensen, Hólder and Young inequalities. Abstract: Inequalities, including fractional integrals, have become a very popular method and have been the main motivation point for many studies in recent years. Studies have been carried out for many types of inequality, thereby introducing a new trend in inequality theory. In this study, new inequalities of Hermite-Hadamard type were obtained by using Atangana-Baleanu integral operators, which provide very useful and effective results with their use in fields such as fractional analysis, applied mathematics, mathematical biology and engineering. The fact that the main results were obtained for functions whose absolute value of the second derivative is convex. In the study, we have proved a new identity for twice differentiable convex functions and the modified version of the integral identity was given in the last section.