On the integral operators pertaining to a family of incomplete <em>I</em>-functions

Manish Kumar Bansal; Devendra Kumar; Manish Kumar Bansal; Devendra Kumar

doi:10.3934/math.2020085

AIMS Mathematics

2020, Volume 5, Issue 2: 1247-1259. doi: 10.3934/math.2020085

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Research article

On the integral operators pertaining to a family of incomplete I-functions

Manish Kumar Bansal ^{1
,
,},
Devendra Kumar ²

1.
Department of Applied Sciences, Government Engineering College,Banswara-327001, Rajasthan, India
2.
Department of Mathematics, University of Rajasthan, Jaipur 302004, Rajasthan, India

Received: 15 October 2019 Accepted: 16 December 2019 Published: 17 January 2020
MSC : Primary: 33B20, 44A10; Secondary: 33E20, 44A40

This paper introduces a new incomplete I-functions. The incomplete I-function is an extension of the I-function given by Saxena ^[1] which is a extension of a familiar Fox's H-function. Next, we find the several interesting classical integral transform of these functions and also find the some basic properties of incomplete I-function. Further, numerous special cases are obtained from our main results among which some are explicitly indicated. Incomplete special functions thus obtained consisting of probability theory has many potential applications which are also presented. Finally, we find the solution of non-homogeneous heat conduction equation in terms of Incomplete I-function.
- Gamma function,
- incomplete Gamma functions,
- incomplete I-functions,
- Mellin-Barnes type contour,
- integral transforms
Citation: Manish Kumar Bansal, Devendra Kumar. On the integral operators pertaining to a family of incomplete I-functions[J]. AIMS Mathematics, 2020, 5(2): 1247-1259. doi: 10.3934/math.2020085

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Abstract

This paper introduces a new incomplete I-functions. The incomplete I-function is an extension of the I-function given by Saxena ^[1] which is a extension of a familiar Fox's H-function. Next, we find the several interesting classical integral transform of these functions and also find the some basic properties of incomplete I-function. Further, numerous special cases are obtained from our main results among which some are explicitly indicated. Incomplete special functions thus obtained consisting of probability theory has many potential applications which are also presented. Finally, we find the solution of non-homogeneous heat conduction equation in terms of Incomplete I-function.

References

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