Dynamical significance of generalized fractional integral inequalities via convexity

• Published in: AIMS mathematics Vol. 6; no. 9; pp. 9705 - 9730
• Main Authors: Ali, Sabila, Mubeen, Shahid, Ali, Rana Safdar, Rahman, Gauhar, Morsy, Ahmed, Nisar, Kottakkaran Sooppy, Purohit, Sunil Dutt, Zakarya, M.
• Format: Journal Article
• Language: English
• Published: AIMS Press 01.01.2021
• Subjects: fractional inequalities; generalized fractional inequalities; hadamard inequality; wright generalized bessel function; η1; η2)-convex function
• ISSN: 2473-6988; 2473-6988
• DOI: 10.3934/math.2021565

The main goal of this paper is to develop the significance of generalized fractional integral inequalities via convex functions. We obtain the new version of fractional integral inequalities with the extended Wright generalized Bessel function acting as a kernel for the convex function, which deals with the Hermite-Hadamard type and trapezoid type inequalities. Moreover, we establish new mid-point type and trapezoid type integral inequalities for (η1,η2)-convex function related to Hermite-Hadamard type inequality. We establish new version of integral inequality for (η1,η2)-convex function related to Fejér type. The results discussed in this paper are a generalized version of many inequalities in literature.