Riemann–Liouville Fractional Integral Form of Modified Baskakov-Type Operators: Approximation Properties and Statistical Convergence

In this paper, a generalized sequence of Baskakov operators connected to the Riemann–Liouville fractional integral is introduced. These sequences of operators deal with smooth approximation behavior in a wider class, i.e., a class of measurable functions in the Lebesgue sense. Further, estimates in terms of test functions and central moments are established. Using the weighted Korovkin-type theorem, uniform convergence in weighted spaces is studied. Additionally, uses of the classical modulus of continuity and Peetre’s K-functional to establish local and global direct approximation theorems are introduced. Lastly, the statistical convergence properties of the suggested operators are investigated. In the last section, theoretical results are supported by numerical examples with graphical and numerical illustrations.