Fractional calculus and applications of family of extended generalized Gauss hypergeometric functions. (English) Zbl 1440.33005
Summary: The aim of the present paper is to establish certain new image formulae of family of some extended generalized Gauss hypergeometric functions by applying the operators of fractional derivative involving \(_2F_1(.)\) due to Saigo. Furthermore, by employing some integral transforms on the resulting formulas, we obtained some more image formulas and also develop a new and further generalized form of the fractional kinetic equation involving the family of some extended generalized Gauss hypergeometric functions and the manifold generality of the family of functions is discussed in terms of the solution of the fractional kinetic equation. The results obtained here are quite general in nature.
MSC:
| 33C20 | Generalized hypergeometric series, \({}_pF_q\) |
| 26A33 | Fractional derivatives and integrals |
| 33E30 | Other functions coming from differential, difference and integral equations |
Keywords:
Pochhammer symbol; fractional calculus; Gauss hypergeometric; Laplace transform; fractional derivative; fractional integrationReferences:
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