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Mathematical Analysis and Applications pp 217–272Cite as

Certain Fractional Integral and Differential Formulas Involving the Extended Incomplete Generalized Hypergeometric Functions

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Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 154))

Abstract

The fractional integral and differential operators involving the family of special functions have found significant importance and applications in various fields of mathematics and engineering. The goal of this chapter is to find the fractional integral and differential formulas (also known as composition formulas) involving the extended incomplete generalized hypergeometric functions by using the generalized fractional calculus operators (the Marichev–Saigo–Maeda operators). After that, we established their image formulas by using the integral transforms like: Beta transform, Laplace transform and Whittaker transform. Moreover, the reduction formulas are also considered as special cases of our main findings associated with the well-known Saigo fractional integral and differential operators, Erdélyi-Kober fractional integral and differential operators, Riemann-Liouville fractional integral and differential operators and the Weyl fractional calculus operators.

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Acknowledgements

This work was supported by a research grant from SERB Project No. TAR/2018/000001 to the first author.

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Authors and Affiliations

  1. International Center for Basic and Applied Sciences, Jaipur, India

    Praveen Agarwal

  2. Department of Mathematics, Anand International College of Engineering, Jaipur, India

    Praveen Agarwal

  3. Department of Mathematics, Harish-Chandra Research Institute (HRI), Allahbad, India

    Praveen Agarwal

  4. Department of Mathematics, Zografou Campus, National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

  5. Department of Mathematics, Mata Sahib Kaur Girls College, Bathinda, India

    Gurmej Singh

  6. Department of Mathematics, Poornima College of Engineering, Jaipur, India

    Shilpi Jain

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  1. Praveen Agarwal
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  1. Department of Mathematics, Zografou Campus, National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

  2. Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, USA

    Panos M. Pardalos

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Agarwal, P., Rassias, T.M., Singh, G., Jain, S. (2019). Certain Fractional Integral and Differential Formulas Involving the Extended Incomplete Generalized Hypergeometric Functions. In: Rassias, T., Pardalos, P. (eds) Mathematical Analysis and Applications. Springer Optimization and Its Applications, vol 154. Springer, Cham. https://doi.org/10.1007/978-3-030-31339-5_8

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