Fractional calculus of modified special functions involving the generalized M-series in their kernels and illustrative examples

Enes Ata; Onur Kıymaz; Praveen Agarwal; Shilpi Jain; Shaher Momani

doi:10.1016/j.padiff.2024.100720

Fractional calculus of modified special functions involving the generalized M-series in their kernels and illustrative examples

Enes Ata
, Onur Kıymaz
, Praveen Agarwal
, Shilpi Jain
, Shaher Momani

Nonlinear Dynamic Research Centre (NDRC)

Kırşehir Ahi Evran University
International College of Engineering
Poornima College of Engineering
University of Jordan

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

3 Scopus citations

Abstract

In this paper we apply the Riemann–Liouville, Erdelyi–Kober and Caputo fractional operators to the modified beta, modified Gauss hypergeometric and modified confluent hypergeometric functions in which the generalized M-series are included in their kernels. Furthermore, as examples, we obtain solutions of some fractional differential equations involving the above modified special functions.

Original language	English
Article number	100720
Journal	Partial Differential Equations in Applied Mathematics
Volume	11
DOIs	https://doi.org/10.1016/j.padiff.2024.100720
State	Published - Sep 2024

Keywords

Beta function
Confluent hypergeometric function
Fractional derivatives and integrals
Fractional differential equations
Gauss hypergeometric function

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10.1016/j.padiff.2024.100720

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abstract = "In this paper we apply the Riemann–Liouville, Erdelyi–Kober and Caputo fractional operators to the modified beta, modified Gauss hypergeometric and modified confluent hypergeometric functions in which the generalized M-series are included in their kernels. Furthermore, as examples, we obtain solutions of some fractional differential equations involving the above modified special functions.",

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AU - Jain, Shilpi

AU - Momani, Shaher

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N2 - In this paper we apply the Riemann–Liouville, Erdelyi–Kober and Caputo fractional operators to the modified beta, modified Gauss hypergeometric and modified confluent hypergeometric functions in which the generalized M-series are included in their kernels. Furthermore, as examples, we obtain solutions of some fractional differential equations involving the above modified special functions.

AB - In this paper we apply the Riemann–Liouville, Erdelyi–Kober and Caputo fractional operators to the modified beta, modified Gauss hypergeometric and modified confluent hypergeometric functions in which the generalized M-series are included in their kernels. Furthermore, as examples, we obtain solutions of some fractional differential equations involving the above modified special functions.

KW - Beta function

KW - Confluent hypergeometric function

KW - Fractional derivatives and integrals

KW - Fractional differential equations

KW - Gauss hypergeometric function

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JO - Partial Differential Equations in Applied Mathematics

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ER -

Fractional calculus of modified special functions involving the generalized M-series in their kernels and illustrative examples

Abstract

Keywords

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