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On Hermite-Hadamard Type Inequalities in Stochastic Fractional Calculus | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 25 آذر 1404 اصل مقاله (396.05 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2025.30980.2689 | ||
| نویسندگان | ||
| Asraa Najm Abood؛ Rawa Khalil Ibrahim* | ||
| Department of Mathematics, College of Dentistry, Diyala University, Diyala, Iraq | ||
| چکیده | ||
| This paper extends Hermite-Hadamard type inequalities within the framework of stochastic fractional calculus. We investigate how fractional integrals, which account for memory effects, interact with random processes. Our work presents three main contributions. First, we provide an error bound for approximating a standard integral of a smooth, deterministic function using stochastic fractional integrals. Second, we extend the well-known Hermite-Hadamard inequality, which applies to convex functions, to the setting of convex stochastic processes, showing how their expected values are bounded by these integrals. Finally, we derive specific mean-square error bounds when approximating a standard Brownian motion using its stochastic fractional integrals. These results enhance our understanding of stochastic fractional inequalities, offering new tools for analyzing complex systems influenced by both memory and randomness. | ||
| کلیدواژهها | ||
| Fractional calculus؛ Stochastic calculus؛ Hermite-Hadamard inequality؛ Riemann- Liouville fractional integral | ||
| مراجع | ||
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[8] N. Sharma, S.K. Mishra, and A. Hamdi, Hermite-Hadamard type inequality for ψ-Riemann-Liouville fractional integrals via preinvex functions, Int. J. Nonlinear Anal. Appl. 13 (2022), no. 1, 3333–3345. https://doi.org/10.22075/ijnaa.2021.21475.2262
[9] J.R. Wang, X. Li, and Y. Zhou, Hermite-Hadamard inequalities involving Riemann-Liouville fractional integrals via ψ-convex functions and applications to special means, Filomat 30 (2016), no. 5, 1143–1150.
[10] T. Zhou and T. Du, Certain fractional integral inclusions pertaining to interval-valued exponential trigonometric convex functions, J. Math. Inequal. 17 (2023), no. 1, 283–314. http://dx.doi.org/10.7153/jmi-2023-17-20 | ||
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