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| On Fractional Hybrid Integral Inequalities via Extended $s$-Convexity |
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| KeyWord:Newton-Cotes inequalities, extended $s$-convex functions, Gauss-Radau formula, $P$-functions, hypergeometric function |
| Author Name | Affiliation | | Badreddine Meftah | Laboratory of Analysis and Control of Differential Equations "ACED", Faculty MISM, Department of Mathematics, University of 8 May 1945 Guelma, P.O. Box 401, 24000 Guelma, Algeria | | Wedad Saleh | Department of Mathematics, College of Science, Taibah University, Al- Medina, Saudi Arabia | | Mohammed Bakheet Almatrafi | Department of Mathematics, College of Science, Taibah University, Al- Medina, Saudi Arabia | | Abdelghani Lakhdari | Department of Mathematics, Faculty of Science and Arts, Kocaeli University, Umuttepe Campus, Kocaeli 41001, T\"{u}rkiye
Laboratory of Energy Systems Technology, National Higher School of Technology and Engineering, Annaba 23005, Algeria |
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| Abstract: |
| 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. |
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