Some Fractional Operators with the Generalized Bessel–Maitland Function

In this paper, we aim to determine some results of the generalized Bessel–Maitland function in the field of fractional calculus. Here, some relations of the generalized Bessel–Maitland functions and the Mittag-Leffler functions are considered. We develop Saigo and Riemann–Liouville fractional integr...

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Main Authors: R. S. Ali, S. Mubeen, I. Nayab, Serkan Araci, G. Rahman, K. S. Nisar
Format: Article
Language:English
Published: Wiley 2020-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2020/1378457
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author R. S. Ali
S. Mubeen
I. Nayab
Serkan Araci
G. Rahman
K. S. Nisar
author_facet R. S. Ali
S. Mubeen
I. Nayab
Serkan Araci
G. Rahman
K. S. Nisar
author_sort R. S. Ali
collection DOAJ
description In this paper, we aim to determine some results of the generalized Bessel–Maitland function in the field of fractional calculus. Here, some relations of the generalized Bessel–Maitland functions and the Mittag-Leffler functions are considered. We develop Saigo and Riemann–Liouville fractional integral operators by using the generalized Bessel–Maitland function, and results can be seen in the form of Fox–Wright functions. We establish a new operator Zν,η,ρ,γ,w,a+μ,ξ,m,σϕ and its inverse operator Dν,η,ρ,γ,w,a+μ,ξ,m,σϕ, involving the generalized Bessel–Maitland function as its kernel, and also discuss its convergence and boundedness. Moreover, the Riemann–Liouville operator and the integral transform (Laplace) of the new operator have been developed.
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institution Kabale University
issn 1026-0226
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language English
publishDate 2020-01-01
publisher Wiley
record_format Article
series Discrete Dynamics in Nature and Society
spelling doaj-art-1e15b0c684ea43faa0b3e82af96d3c962025-08-20T03:54:34ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2020-01-01202010.1155/2020/13784571378457Some Fractional Operators with the Generalized Bessel–Maitland FunctionR. S. Ali0S. Mubeen1I. Nayab2Serkan Araci3G. Rahman4K. S. Nisar5Department of Mathematics, University of Sargodha, Sargodha, PakistanDepartment of Mathematics, University of Sargodha, Sargodha, PakistanDepartment of Mathematics, University of Sargodha, Sargodha, PakistanDepartment of Economics, Faculty of Economics, Administrative and Social Sciences, Hasan Kalyoncu University, TR-27410 Gaziantep, TurkeyDepartment of Mathematics, Shaheed Benazir Bhutto University, Sheringal, PakistanDepartment of Mathematics, College of Arts and Sciences, Prince Sattam Bin Abdulaziz University, Wadi Aldawaser 11991, Saudi ArabiaIn this paper, we aim to determine some results of the generalized Bessel–Maitland function in the field of fractional calculus. Here, some relations of the generalized Bessel–Maitland functions and the Mittag-Leffler functions are considered. We develop Saigo and Riemann–Liouville fractional integral operators by using the generalized Bessel–Maitland function, and results can be seen in the form of Fox–Wright functions. We establish a new operator Zν,η,ρ,γ,w,a+μ,ξ,m,σϕ and its inverse operator Dν,η,ρ,γ,w,a+μ,ξ,m,σϕ, involving the generalized Bessel–Maitland function as its kernel, and also discuss its convergence and boundedness. Moreover, the Riemann–Liouville operator and the integral transform (Laplace) of the new operator have been developed.http://dx.doi.org/10.1155/2020/1378457
spellingShingle R. S. Ali
S. Mubeen
I. Nayab
Serkan Araci
G. Rahman
K. S. Nisar
Some Fractional Operators with the Generalized Bessel–Maitland Function
Discrete Dynamics in Nature and Society
title Some Fractional Operators with the Generalized Bessel–Maitland Function
title_full Some Fractional Operators with the Generalized Bessel–Maitland Function
title_fullStr Some Fractional Operators with the Generalized Bessel–Maitland Function
title_full_unstemmed Some Fractional Operators with the Generalized Bessel–Maitland Function
title_short Some Fractional Operators with the Generalized Bessel–Maitland Function
title_sort some fractional operators with the generalized bessel maitland function
url http://dx.doi.org/10.1155/2020/1378457
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