Extended Bessel-Maitland function and its properties pertaining to integral transforms and fractional calculus

D. L. Suthar; A. M. Khan; A. Alaria; S. D. Purohit; J. Singh; D. L. Suthar; A. M. Khan; A. Alaria; S. D. Purohit; J. Singh

doi:10.3934/math.2020096

AIMS Mathematics

2020, Volume 5, Issue 2: 1400-1410. doi: 10.3934/math.2020096

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Research article

Extended Bessel-Maitland function and its properties pertaining to integral transforms and fractional calculus

1.
Department of Mathematics, Wollo University, P. O. Box: 1145, Dessie, Ethiopia
2.
Department of Mathematics, JIET Group of Institutions, Jodhpur, Rajasthan, India
3.
Department of Mathematics, Poornima University, Jaipur, 303905, India
4.
Department of HEAS(Mathematics), Rajasthan Technical University, Kota-324010, India
5.
Department of Mathematics, JECRC University, Jaipur-303905, India

Received: 12 November 2019 Accepted: 02 January 2020 Published: 20 January 2020
MSC : Primary: 26A33; Secondary: 33C20, 44A10, 44A20

The aim of this paper is to establish an (presumably new) extension of generalized Bessel-Maitland function by using the extension of extended beta function. In addition, investigate several important properties namely integral representation, derivatives, recurrence relation, Beta transform and Mellin transform. Further, certain properties of the Riemann-Liouville fractional calculus associated with extended generalized Bessel-Maitland function are also investigated.
- extended Bessel-Maitland function,
- extended beta function,
- integral transform,
- Riemann-Liouville fractional calculus operators
Citation: D. L. Suthar, A. M. Khan, A. Alaria, S. D. Purohit, J. Singh. Extended Bessel-Maitland function and its properties pertaining to integral transforms and fractional calculus[J]. AIMS Mathematics, 2020, 5(2): 1400-1410. doi: 10.3934/math.2020096

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Abstract

The aim of this paper is to establish an (presumably new) extension of generalized Bessel-Maitland function by using the extension of extended beta function. In addition, investigate several important properties namely integral representation, derivatives, recurrence relation, Beta transform and Mellin transform. Further, certain properties of the Riemann-Liouville fractional calculus associated with extended generalized Bessel-Maitland function are also investigated.

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