Weighted Fractional Calculus: A General Class of Operators

We conduct a formal study of particular class fractional operators, namely weighted calculus, and its extension to the more general known as calculus with respect functions. emphasise importance conjugation relationships classical Riemann–Liouville use them prove many fundamental properties these operators. As examples, we consider special cases such tempered, Hadamard-type, Erdélyi–Kober also define appropriate modifications Laplace transform convolution operations, solve some ordinary differential equations in setting classes