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Deriving Hermite–Hadamard-Type Inequalities via Stochastic k-Caputo Fractional Derivatives
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Department of Mathematics, College of Science, Jouf University, P.O. Box 2014, Sakaka 72388, Saudi Arabia
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Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
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Department of Mathematics, College of Science and Humanities, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
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Mathematics Education Section Faculty of Education and Arts, Sohar University, P.O. Box 44, Sohar 311, Oman
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Department of Mathematics, Faculty of sciences of Sfax, Sfax University, Sfax 3029, Tunisia
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Authors to whom correspondence should be addressed.
Fractal Fract. 2025, 9(12), 757; https://doi.org/10.3390/fractalfract9120757 (registering DOI)
Submission received: 9 October 2025
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Revised: 15 November 2025
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Accepted: 18 November 2025
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Published: 22 November 2025
Abstract
By leveraging the concept of k-Caputo fractional derivatives for stochastic processes, in this paper, we derive a generalized Hermite–Hadamard inequality tailored to n-times differentiable convex stochastic processes, providing a powerful tool for analyzing systems governed by fractional dynamics in probabilistic settings. Additionally, we establish two new integral identities that serve as the foundation for developing midpoint- and trapezium-type inequalities for -times differentiable convex stochastic processes. These results not only enrich the theoretical underpinnings of fractional calculus, but also offer practical implications for modeling and understanding complex systems with memory and randomness. The proposed framework opens new avenues for future research in stochastic analysis and fractional calculus, with potential applications in fields such as financial mathematics, engineering, and physics.
Share and Cite
MDPI and ACS Style
Alruwaily, Y.; Fakhfakh, R.; Alomani, G.; Alzahrani, R.; Ben Makhlouf, A.
Deriving Hermite–Hadamard-Type Inequalities via Stochastic k-Caputo Fractional Derivatives. Fractal Fract. 2025, 9, 757.
https://doi.org/10.3390/fractalfract9120757
AMA Style
Alruwaily Y, Fakhfakh R, Alomani G, Alzahrani R, Ben Makhlouf A.
Deriving Hermite–Hadamard-Type Inequalities via Stochastic k-Caputo Fractional Derivatives. Fractal and Fractional. 2025; 9(12):757.
https://doi.org/10.3390/fractalfract9120757
Chicago/Turabian Style
Alruwaily, Ymnah, Raouf Fakhfakh, Ghadah Alomani, Rabab Alzahrani, and Abdellatif Ben Makhlouf.
2025. "Deriving Hermite–Hadamard-Type Inequalities via Stochastic k-Caputo Fractional Derivatives" Fractal and Fractional 9, no. 12: 757.
https://doi.org/10.3390/fractalfract9120757
APA Style
Alruwaily, Y., Fakhfakh, R., Alomani, G., Alzahrani, R., & Ben Makhlouf, A.
(2025). Deriving Hermite–Hadamard-Type Inequalities via Stochastic k-Caputo Fractional Derivatives. Fractal and Fractional, 9(12), 757.
https://doi.org/10.3390/fractalfract9120757
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