TY - JOUR
T1 - Some new fractional corrected Euler-Maclaurin type inequalities for function whose second derivatives are s-convex function
AU - Munir, Arslan
AU - Vivas-Cortez, Miguel
AU - Qayyum, Ather
AU - Budak, Hüseyin
AU - Faiz, Irza
AU - Supadi, Siti Suzlin
N1 - Publisher Copyright:
© 2024 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.
PY - 2024
Y1 - 2024
N2 - Fractional integrals and inequalities have gained a lot of attention in recent years. By introducing innovative analytical approaches and applications, and by applying these approaches, numerous forms of inequalities have been examined. In this paper, we establish new identity for the twice differentiable function where the absolute value is convex. By utilizing this identity, numerous Corrected Euler-Maclaurin-type inequalities are developed for the Caputo-Fabrizio fractional integral operator. Based on this identity, the Corrected Euler-Maclaurin-type inequalities for (Formula presented.) -convex function are obtained. By employing well-known inequalities such as Hölder’s and Power -Mean, we are introduced several new error bounds and estimates for Corrected Euler-Maclaurin-type inequalities. Additionally, special cases of the present results are applied to obtain the previous well-known results.
AB - Fractional integrals and inequalities have gained a lot of attention in recent years. By introducing innovative analytical approaches and applications, and by applying these approaches, numerous forms of inequalities have been examined. In this paper, we establish new identity for the twice differentiable function where the absolute value is convex. By utilizing this identity, numerous Corrected Euler-Maclaurin-type inequalities are developed for the Caputo-Fabrizio fractional integral operator. Based on this identity, the Corrected Euler-Maclaurin-type inequalities for (Formula presented.) -convex function are obtained. By employing well-known inequalities such as Hölder’s and Power -Mean, we are introduced several new error bounds and estimates for Corrected Euler-Maclaurin-type inequalities. Additionally, special cases of the present results are applied to obtain the previous well-known results.
KW - Euler-Maclaurin-type inequalities
KW - corrected Euler-Maclaurin-type inequalities
KW - fractional integrals
KW - power-mean inequality
KW - s-convex function
UR - http://www.scopus.com/inward/record.url?scp=85196431896&partnerID=8YFLogxK
U2 - 10.1080/13873954.2024.2356698
DO - 10.1080/13873954.2024.2356698
M3 - Article
AN - SCOPUS:85196431896
SN - 1387-3954
VL - 30
SP - 543
EP - 566
JO - Mathematical and Computer Modelling of Dynamical Systems
JF - Mathematical and Computer Modelling of Dynamical Systems
IS - 1
ER -