Ali, Muhammad AamirKara, HasanTariboon, JessadaAsawasamrit, SuphawatBudak, HüseyinHezenci, Fatih2023-07-262023-07-2620212073-8994https://doi.org/10.3390/sym13122249https://hdl.handle.net/20.500.12684/12539From the past to the present, various works have been dedicated to Simpson's inequality for differentiable convex functions. Simpson-type inequalities for twice-differentiable functions have been the subject of some research. In this paper, we establish a new generalized fractional integral identity involving twice-differentiable functions, then we use this result to prove some new Simpson's-formula-type inequalities for twice-differentiable convex functions. Furthermore, we examine a few special cases of newly established inequalities and obtain several new and old Simpson's-formula-type inequalities. These types of analytic inequalities, as well as the methodologies for solving them, have applications in a wide range of fields where symmetry is crucial.en10.3390/sym13122249info:eu-repo/semantics/openAccessSimpson-Type Inequalities; Convex Function; Fractional IntegralsHermite-Hadamard Inequalities; Integral-Inequalities; ExtensionsArticle13122-s2.0-85120403175WOS:000737213400001Q2Q2