Generalization of Hermite-Hadamard Integral Inequality via Caputo Fabrizio Fractional Integral Operator

Authors

  • Ajab Ali Department of Basic Sciences and Related Studies, Mehran UET, Jamshoro, Pakistan
  • Muhammad Tariq Mathematics Research Center, Near East University, Near East Boulevard, 99138, Nicosia /Mersin, Turkey
  • Asif Ali Shaikh 1Department of Basic Sciences and Related Studies, Mehran UET, Jamshoro, Pakistan
  • Hijaz Ahmad Near East University, Operational Research Center in Healthcare, TRNC Mersin 10, Nicosia, 99138, Turkey
  • Clemente Cesarano Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39,00186 Roma, Italy

DOI:

https://doi.org/10.48165/gjs.2025.2202

Keywords:

Preinvexity, H-H inequality, Caputo-Fabrizio Operator

Abstract

Certainly, fractional calculus has grabbed the keen interest of numerous investigators in the last couple of decades. Numerous real-world problems and demonstrations have involved the development of the Caputo-Fabrizio fractional operator. Our article’s primary goal is to enhance Hermite-Hadamard (H-H) integral inequality and its generalizations by applying the Caputo-Fabrizio fractional integral operator (CFFIO) and the preinvexity concept. We additionally offer some applications of our key findings to specific methods. 

 

Author Biographies

  • Muhammad Tariq, Mathematics Research Center, Near East University, Near East Boulevard, 99138, Nicosia /Mersin, Turkey

    Department of Mathematics, Balochistan Residential College, Loralai, Balochistan, Pakistan

  • Hijaz Ahmad, Near East University, Operational Research Center in Healthcare, TRNC Mersin 10, Nicosia, 99138, Turkey

    Department of Mathematics, College of Science, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul 02841, South Korea 

     

References

Ahmad, H., Khokhar, R., Tariq, M., Suleman, M., Ntouyas, S. K., & Tariboon, J. (2023). Some new notions of fractional Hermite-Hadamard type inequalities involving applications to the physical sciences. Journal of Mathematics and Computer Science, 33(1), 27–41.

Tariq, M., Ntouyas, S. K., & Shaikh, A. A. (2023). A comprehensive review of the Hermite-Hadamard inequality pertaining to Quantum Calculus. Foundations, 3, 340–379.

Tariq, M., Shaikh, A. A., Ntouyas, S. K., & Tariboon, J. (2023). A comprehensive review of the Hermite-Hadamard inequality pertaining to fractional differential operators. Surveys in Mathematics and its Applications, 18, 223–257.

Tariq, M., Ntouyas, S. K., & Shaikh, A. A. (2023). A comprehensive review of the Hermite–Hadamard inequality pertaining to fractional integral operators. Mathematics, 11, 1953.

Tariq, M., Sahoo, S. K., & Ntouyas, S. K. (2023). Some refinements of Hermite–Hadamard type Integral inequalities involving refined convex function of the Raina type. Axioms, 12, 124.

Tariq, M., Shaikh, A. S., & Ntouyas, S. K. (2023). Some new fractional Hadamard and Pachpatte type inequalities with applications via generalized preinvexity. Symmetry, 15, 1033.

Ahmad, H., Tariq, M., Sahoo, S. K., Baili, J., & Cesarano, C. (2021). New estimations of Hermite-Hadamard type integral inequalities for special functions. Fractal and Fractional, 5, 144.

Cortez, M. J. V., Liko, R., Kashuri, A., & Hernández, J. E. H. (2019). New quantum estimates of trapezium-type inequalities for generalized ϕ–convex functions. Mathematics, 7, 1047.

Cortez, M. J. V., Kashuri, A., & Hernández, J. E. H. (2020). Trapezium-type inequalities for Raina’s fractional integrals operator using generalized convex functions. Mathematics, 12, 1034.

Du, T. S., Liao, J. G., Chen, L. G., & Awan, M. U. (2016). Properties and Riemann–Liouville fractional Hermite–Hadamard inequalities for the generalized (α, m)-preinvex functions. Journal of Inequalities and Applications, 2016, 306.

Du, T. T., Liao, J. G., & Li, Y. J. (2016). Properties and integral inequalities of Hadamard-Simpson type for the generalized (s, m)–preinvex functions. Journal of Nonlinear Science and Applications, 9, 3112–3126.

Barani, A., Ghazanfari, G., & Dragomir, S. S. (2012). Hermite-Hadamard inequality for functions whose derivatives absolute values are preinvex. Journal of Inequalities and Applications, 2012, 247.

Du, T. T., Liao, J. G., & Li, Y. J. (2016). Properties and integral inequalities of Hadamard-Simpson type for the generalized (s, m)–preinvex functions. Journal of Nonlinear Science and Applications, 9, 3112–3126.

Weir, T., & Mond, B. (1988). Preinvex functions in multiple-objective optimization. Journal of Mathematical Analysis and Applications, 136, 29–38.

Deng, Y., Kalsoom, H., & Wu, S. (2019). Some new Quantum Hermite–Hadamard-type estimates within a class of generalized (s, m)—preinvex functions. Symmetry, 11, 1283.

Farajzadeh, A., Noor, M. A., & Noor, K. I. (2009). Vector nonsmooth variational-like inequalities and optimization problems. Nonlinear Analysis, 71, 3471–3476.

Noor, M. A. (1994). Variational–like inequalities. Optimization, 30, 323–330.

Mitrinovic, D. S., Pecaric, J. E., & Fink, A. M. (1993). Classical and New Inequalities in Analysis. Kluwer Academic.

Caputo, M., & Fabrizio, M. (2015). A new definition of fractional derivative without singular kernel. Progress in Fractional Differentiation and Applications, 1, 73–85.

Published

2025-10-08

How to Cite

Generalization of Hermite-Hadamard Integral Inequality via Caputo Fabrizio Fractional Integral Operator. (2025). Global Journal of Sciences, 2(2), 15-22. https://doi.org/10.48165/gjs.2025.2202