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New Extension of Fractional-Calculus Results Associated with Product of Certain Special Functions

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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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Acknowledgements

The authors are very grateful to the anonymous referees for carefully reading the article and for their constructive comments and suggestions which have improved the article.

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Authors and Affiliations

  1. Department of Mathematics, Malaviya National Institute of Technology, Jaipur, Rajasthan, 302017, India

    Sanjay Bhatter & Amit Mathur

  2. Department of Mathematics, University of Rajasthan, Jaipur, Rajasthan, 302004, India

    Devendra Kumar

  3. Department of Mathematics, JECRC University, Jaipur, Rajasthan, 303905, India

    Jagdev Singh

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  1. Sanjay Bhatter
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  2. Amit Mathur
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  4. Jagdev Singh
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All the authors have worked equally in this manuscript. All the four authors have read and approved the final manuscript.

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Correspondence to Jagdev Singh.

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Bhatter, S., Mathur, A., Kumar, D. et al. New Extension of Fractional-Calculus Results Associated with Product of Certain Special Functions. Int. J. Appl. Comput. Math 7, 97 (2021). https://doi.org/10.1007/s40819-021-01007-4

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