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Volume 7, Issue 4
On Fractional Hybrid Integral Inequalities via Extended $s$-Convexity

Badreddine Meftah, Wedad Saleh, Mohammed Bakheet Almatrafi & Abdelghani Lakhdari

DOI: 10.12150/jnma.2025.1153

J. Nonl. Mod. Anal., 7 (2025), pp. 1153-1178.

Published online: 2025-07

[An open-access article; the PDF is free to any online user.]

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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.

  • Keywords

Newton-Cotes inequalities, extended $s$-convex functions, Gauss-Radau formula, $P$-functions, hypergeometric function.

  • AMS Subject Headings

26D10, 26D15, 26A51

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-7-1153, author = {Meftah , BadreddineSaleh , WedadAlmatrafi , Mohammed Bakheet and Lakhdari , Abdelghani}, title = {On Fractional Hybrid Integral Inequalities via Extended $s$-Convexity}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2025}, volume = {7}, number = {4}, pages = {1153--1178}, 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.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2025.1153}, url = {http://global-sci.org/intro/article_detail/jnma/24230.html} }
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 -

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.

Meftah , BadreddineSaleh , WedadAlmatrafi , Mohammed Bakheet and Lakhdari , Abdelghani. (2025). On Fractional Hybrid Integral Inequalities via Extended $s$-Convexity. Journal of Nonlinear Modeling and Analysis. 7 (4). 1153-1178. doi:10.12150/jnma.2025.1153
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