Extended Caputo fractional derivative operator

R. P. Agarwal; P. Agarwal

Extended Caputo fractional derivative operator

R. P. Agarwal
, P. Agarwal

Texas A&M University-Kingsville
International College of Engineering

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

The principle aim of this paper is devoted to present an extended Caputo fractional derivative operator involving the generalized hypergeometric type function F_p^{(α, β; κ μ)} (a, b; c; z) introduced by Srivastava et al. and investigate some of its properties. In the sequel, extensions of some hypergeometric functions and their integral representations are also presented by using the extended fractional derivative operator. Furthermore, linear and bilinear generating relations for the extended hypergeometric functions are obtained, and Mellin transforms of some extended hypergeometric functions and fractional derivatives are also determined.

Original language	English
Pages (from-to)	301-316
Number of pages	16
Journal	Advanced Studies in Contemporary Mathematics (Kyungshang)
Volume	25
Issue number	3
State	Published - 1 Jul 2015
Externally published	Yes

Keywords

Beta function
Caputo Fractional derivative
Fox H-function
Gamma function
Generating functions
Hypergeometric functions
Integral representations
Mellin transform

Cite this

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abstract = "The principle aim of this paper is devoted to present an extended Caputo fractional derivative operator involving the generalized hypergeometric type function Fp(α, β; κ μ) (a, b; c; z) introduced by Srivastava et al. and investigate some of its properties. In the sequel, extensions of some hypergeometric functions and their integral representations are also presented by using the extended fractional derivative operator. Furthermore, linear and bilinear generating relations for the extended hypergeometric functions are obtained, and Mellin transforms of some extended hypergeometric functions and fractional derivatives are also determined.",

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AB - The principle aim of this paper is devoted to present an extended Caputo fractional derivative operator involving the generalized hypergeometric type function Fp(α, β; κ μ) (a, b; c; z) introduced by Srivastava et al. and investigate some of its properties. In the sequel, extensions of some hypergeometric functions and their integral representations are also presented by using the extended fractional derivative operator. Furthermore, linear and bilinear generating relations for the extended hypergeometric functions are obtained, and Mellin transforms of some extended hypergeometric functions and fractional derivatives are also determined.

KW - Beta function

KW - Caputo Fractional derivative

KW - Fox H-function

KW - Gamma function

KW - Generating functions

KW - Hypergeometric functions

KW - Integral representations

KW - Mellin transform

UR - https://www.scopus.com/pages/publications/84941947674

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SN - 1229-3067

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SP - 301

EP - 316

JO - Advanced Studies in Contemporary Mathematics (Kyungshang)

JF - Advanced Studies in Contemporary Mathematics (Kyungshang)

IS - 3

ER -

Extended Caputo fractional derivative operator

Abstract

Keywords

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