TY - JOUR
T1 - Fractional integral inequalities and error estimates of generalized mean differences
AU - Samraiz, Muhammad
AU - Ghaffar, Muhammad Tanveer
AU - Naheed, Saima
AU - Vivas-Cortez, Miguel
N1 - Publisher Copyright:
© 2024 The Author(s)
PY - 2024/3/26
Y1 - 2024/3/26
N2 - In this research, we focus on a novel class of mean inequalities involving Riemann-Liouville fractional integrals. We employ these integrals to investigate various fundamental identities that help us to explore mean inequalities. By utilizing a generalized concept of convexity, we establish a unique set of these problems. To ensure the accuracy of our findings, we generate 2D and 3D graphs accompanied by corresponding numerical data using specific functions, effectively illustrating the inequalities. Furthermore, it is easy to observe that some known results from previous studies manifest as special cases of our primary outcomes. This approach enables us to substantiate the validity of our findings and strengthen our conclusions. The connection of the main finding with the context of statistics and mathematics is provided, playing a significant role in addressing real-life problems.
AB - In this research, we focus on a novel class of mean inequalities involving Riemann-Liouville fractional integrals. We employ these integrals to investigate various fundamental identities that help us to explore mean inequalities. By utilizing a generalized concept of convexity, we establish a unique set of these problems. To ensure the accuracy of our findings, we generate 2D and 3D graphs accompanied by corresponding numerical data using specific functions, effectively illustrating the inequalities. Furthermore, it is easy to observe that some known results from previous studies manifest as special cases of our primary outcomes. This approach enables us to substantiate the validity of our findings and strengthen our conclusions. The connection of the main finding with the context of statistics and mathematics is provided, playing a significant role in addressing real-life problems.
KW - Error estimates
KW - Fractional integrals
KW - Generalized means
KW - Hölder's inequality
KW - Mean-type inequalities
UR - http://www.scopus.com/inward/record.url?scp=85188806039&partnerID=8YFLogxK
U2 - 10.1016/j.aej.2024.03.027
DO - 10.1016/j.aej.2024.03.027
M3 - Article
AN - SCOPUS:85188806039
SN - 1110-0168
VL - 94
SP - 172
EP - 192
JO - Alexandria Engineering Journal
JF - Alexandria Engineering Journal
ER -