TY - CHAP
T1 - Certain Fractional Integral and Differential Formulas Involving the Extended Incomplete Generalized Hypergeometric Functions
AU - Agarwal, Praveen
AU - Rassias, Themistocles M.
AU - Singh, Gurmej
AU - Jain, Shilpi
N1 - Publisher Copyright:
© 2019, Springer Nature Switzerland AG.
PY - 2019
Y1 - 2019
N2 - 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.
AB - 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.
KW - Erdélyi-Kober fractional calculus operators
KW - Extended incomplete generalized hypergeometric function
KW - Fractional differential operators
KW - Fractional integral operators
KW - Gamma function
KW - Incomplete gamma Function
KW - Pochhammer symbol
KW - Riemann-Liouville fractional calculus operators
KW - Saigo fractional integral and differential operators
KW - Weyl fractional integral operator and differential operators
UR - https://www.scopus.com/pages/publications/85076749837
U2 - 10.1007/978-3-030-31339-5_8
DO - 10.1007/978-3-030-31339-5_8
M3 - Chapter
AN - SCOPUS:85076749837
T3 - Springer Optimization and Its Applications
SP - 217
EP - 272
BT - Springer Optimization and Its Applications
PB - Springer
ER -