Kara, Mustafa2022-12-292022-12-292022https://doi.org/10.31801/cfsuasmas.1067635http://hdl.handle.net/20.500.12575/86626In the present paper, we introduce the fractional q-integral of Riemann-Liouville integral type Szász-Mirakyan-Kantorovich operators. Korovkin-type approximation theorem is given and the order of convergence of these operators are obtained by using Lipschitz-type maximal functions, second order modulus of smoothness and Peetre's K-functional. Weighted approximation properties of these operators in terms of modulus of continuity have been investigated. Then, for these operators, we give a Voronovskaya-type theorem. Moreover, bivariate fractional q- integral Riemann-Liouville fractional integral type Szász-Mirakyan-Kantorovich operators are constructed. The last section is devoted to detailed graphical representation and error estimation results for these operators.enSzasz-Mirakyan-Kantorovich operators, q-integral of Riemann-Liouville, Voronovskaya-typeArticle714113611681303-5991