Exploring multi-index functions with significance relations and associated with general properties in fractional calculus

The extensions and generalization of the special functions including in particular Pochhammer symbol, hypergeometric functions, Mittag-Leffler type functions, and Bessel-Maitland functions are the main core for the development of fractional operators by means of its kernel.We present a new extension of the multi-inde Mittag Leffler (MML) function and multiindex Bessel-Maitland (MBM) function by using the generalized Pochhammer symbol.Moreover, we establish some significance relations of such type of multi-index functions with other existing versions of Mittag-Leffler and Bessel-Maitland functions.Moreover, we analyze the behavior of some well-known fractional operators like as Saigo's fractional integral (SFI), Erdeyli fractional integral (EFI) and Riemann fractional integral (RFI) with the product of newly describe multi-index functions.