| Citation: |
Man Huang, Jianmiao Ruan. ERROR BOUNDS FOR RIEMANN-LIOUVILLE FRACTIONAL INTEGRALS VIA STRONGLY H-CONVEX FUNCTIONS WITH HIGHER ORDER DERIVATIVES[J]. Journal of Applied Analysis & Computation, 2027, 17(2): 652-680. doi: 10.11948/20260108
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ERROR BOUNDS FOR RIEMANN-LIOUVILLE FRACTIONAL INTEGRALS VIA STRONGLY H-CONVEX FUNCTIONS WITH HIGHER ORDER DERIVATIVES
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Abstract
This paper is devoted to establishing new general identities associated with Riemann–Liouville fractional integrals for $ n $-times differentiable functions. By employing these identities, we derive a series of midpoint- and trapezoid-type error bounds for approximations involving such fractional operators. A key feature of our analysis is the assumption that the $ q $-th power of the $ n $-th derivative of the function under consideration is strongly $ h $-convex. This approach yields estimates that depend not only on the behavior of the function at the endpoints of the interval but also on an interior point, thereby offering enhanced generality. Our results unify and extend several inequalities previously established in the literature for convex, $ s $-convex, and $ h $-convex functions in the context of fractional integrals.
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Man Huang, Jianmiao Ruan. ERROR BOUNDS FOR RIEMANN-LIOUVILLE FRACTIONAL INTEGRALS VIA STRONGLY H-CONVEX FUNCTIONS WITH HIGHER ORDER DERIVATIVES[J]. Journal of Applied Analysis & Computation, 2027, 17(2): 652-680. doi: 10.11948/20260108
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