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

In: Mathematical Analysis and Applications

Author

Listed:
  • Praveen Agarwal

    (International Center for Basic and Applied Sciences
    Anand International College of Engineering
    Harish-Chandra Research Institute (HRI))

  • Themistocles M. Rassias

    (National Technical University of Athens)

  • Gurmej Singh

    (Mata Sahib Kaur Girls College)

  • Shilpi Jain

    (Poornima College of Engineering)

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.

Suggested Citation

  • Praveen Agarwal & Themistocles M. Rassias & Gurmej Singh & Shilpi Jain, 2019. "Certain Fractional Integral and Differential Formulas Involving the Extended Incomplete Generalized Hypergeometric Functions," Springer Optimization and Its Applications, in: Themistocles M. Rassias & Panos M. Pardalos (ed.), Mathematical Analysis and Applications, pages 217-272, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-31339-5_8
    DOI: 10.1007/978-3-030-31339-5_8
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