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: | , , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| 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. |
| format | Article |
| id | doaj-art-1e15b0c684ea43faa0b3e82af96d3c96 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| 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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