Abstract
Fractional order calculus and special functions play a great role in scientific, financial and technological fields. In view of considerable impact and applications of fractional derivatives and integrals in real life, we aim to suggest some main formulas for the product of generalized M-series, $${\overline{\text{H}}}$$ -function and Aleph function associated with the Riemann-Liouvillle, the Weyl and many other operators of fractional order, which are derived by using the concept of the Cauchy-Goursat integral formula. The formulas derived in the present study can be employed to examine a broad class of new and known formulas involving simpler special functions, hitherto scattered in the literature.
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