Lakhdari, AbdelghaniSarikaya, Mehmet ZekiBudak, HuseyinMeftah, Badreddine2026-07-012026-07-0120262307-41082307-4116https://doi.org/10.1016/j.kjs.2025.100515https://hdl.handle.net/20.500.12684/23574Tempered fractional integrals offer a flexible and physically realistic extension of classical fractional operators by incorporating an exponential tempering factor that attenuates long-range memory effects. This modification not only ensures better convergence and numerical stability but also allows for more accurate modeling of real-world phenomena such as anomalous diffusion, financial returns, or geophysical processes, where power-law behaviors are observed but truncated at large scales. This study advances Bullen-type inequalities within the framework of tempered fractional calculus. By formulating a novel identity based on tempered operators, we derive generalized estimates applicable to various function classes, including those with convex or bounded derivatives, r-L-H & ouml;lderian functions, and functions of bounded variation. The inclusion of exponential tempering parameters refines classical Bullen results by balancing non-local effects with convergence guarantees. To illustrate their applicability, these bounds are applied to special means, highlighting how convexity constraints help stabilize tempered fractional integrals in practical contexts.en10.1016/j.kjs.2025.100515info:eu-repo/semantics/openAccessTempered Fractional IntegralsBullen-Type InequalitiesConvex FunctionsR-L-H & Ouml;Lderian FunctionsFunctions Of Bounded VariationYoung'S InequalityArticle5312-s2.0-105023437843WOS:001630511000001Q2Q30000-0003-2943-26780000-0002-6165-92420000-0001-8843-955X0000-0001-8843-955X