Fractional‐type integral operators and their applications to trend estimation of COVID‐19.

In this paper, we construct a novel family of fractional‐type integral operators of a function f$$ f $$ by replacing sample values (f(k/n))k=0n$$ {\left(f\left(k/n\right)\right)}_{k=0}^n $$ with the fractional mean values of that function. We give some explicit formulas for higher order moments of the proposed operators and investigate some approximation properties. We also define the fractional variants of Mirakyan–Favard–Szász and Baskakov‐type operators and calculate the higher order moments of these operators. We give an explicit formula for fractional derivatives of proposed operators with the help of the Caputo‐type fractional derivative Furthermore, several graphical and numerical results are presented in detail to demonstrate the accuracy, applicability, and validity of the proposed operators. Finally, an illustrative real‐world example associated with the recent trend of Covid‐19 has been investigated to demonstrate the modeling capabilities of fractional‐type integral operators. [ABSTRACT FROM AUTHOR]