Budak, HüseyinErtuğral, FatmaAli, Muhammad AamirBilişik, Özge NalanSarıkaya, Mehmet ZekiNonlaopon, Kamsing2023-07-262023-07-2620222473-6988https://doi.org/10.3934/math.2023094https://hdl.handle.net/20.500.12684/12547In this paper, we establish an integral identity involving differentiable functions and generalized fractional integrals. Then, using the newly established identity, we prove some new general versions of Bullen and trapezoidal type inequalities for differentiable convex functions. The main benefit of the newly established inequalities is that they can be converted into similar inequalities for classical integrals, Riemann-Liouville fractional integrals, k-Riemann-Liouville fractional integrals, Hadamard fractional integrals, etc. Moreover, the inequalities presented in the paper are extensions of several existing inequalities in the literature.en10.3934/math.2023094info:eu-repo/semantics/openAccessHermite-Hadamard Inequality; Fractional Integral Operators; Convex FunctionHadamard-Type Inequalities; Hermite-Hadamard; Differentiable Mappings; Real NumbersArticle81183318472-s2.0-85140204049WOS:000877736600007Q2Q1