TY - JOUR
T1 - On Fractional Hybrid Integral Inequalities via Extended $s$-Convexity
AU - Meftah , Badreddine
AU - Saleh , Wedad
AU - Almatrafi , Mohammed Bakheet
AU - Lakhdari , Abdelghani
JO - Journal of Nonlinear Modeling and Analysis
VL - 4
SP - 1153
EP - 1178
PY - 2025
DA - 2025/07
SN - 7
DO - http://doi.org/10.12150/jnma.2025.1153
UR - https://global-sci.org/intro/article_detail/jnma/24230.html
KW - Newton-Cotes inequalities, extended $s$-convex functions, Gauss-Radau formula, $P$-functions, hypergeometric function.
AB - <p style="text-align: justify;">In this study, we introduce a novel hybrid identity that successfully
combines Newton-Cotes and Gauss quadratures, enabling us to recover both
Simpson’s second formula and the left and right Radau 2 point rules, among
others. Based on this versatile foundation, we establish some new biparametric fractional integral inequalities for functions whose first derivatives are
extended $s$-convex in the second sense. To support our findings, we present
illustrative examples featuring graphical representations and conclude with
several practical applications to demonstrate the effectiveness of our results.</p>