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

Praveen Agarwal (), Themistocles M. Rassias (), Gurmej Singh () and Shilpi Jain ()
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Praveen Agarwal: International Center for Basic and Applied Sciences
Themistocles M. Rassias: National Technical University of Athens
Gurmej Singh: Mata Sahib Kaur Girls College
Shilpi Jain: Poornima College of Engineering

A chapter in Mathematical Analysis and Applications, 2019, pp 217-272 from Springer

Abstract: 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.

Keywords: Fractional integral operators; Fractional differential operators; Saigo fractional integral and differential operators; Erdélyi-Kober fractional calculus operators; Riemann-Liouville fractional calculus operators; Weyl fractional integral operator and differential operators; Incomplete gamma Function; Extended incomplete generalized hypergeometric function; Pochhammer symbol; Gamma function; Primary 33B20, 44A20, 65R10; Secondary 26A33, 33C20 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/978-3-030-31339-5_8

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