Multi-parameter generalized fractional operators and their integral transforms

In this chapter, we introduce three types of multi-parameter generalized fractional operators in the sense of the Riemann–Liouville and Caputo fractional operators, which contain generalized M-series in their kernels. These fractional operators have a more general form than many fractional operators in the literature. We also obtain the Laplace, Mellin, and beta integral transforms of these fractional operators and give some illustrative examples. Finally, we present the relations of these operators to fractional operators in the literature.