Estimation of generalized fractional integral operators with nonsingular function as a kernel

Iqra Nayab; Shahid Mubeen; Rana Safdar Ali; Gauhar Rahman; Abdel-Haleem Abdel-Aty; Emad E. Mahmoud; Kottakkaran Sooppy Nisar; Iqra Nayab; Shahid Mubeen; Rana Safdar Ali; Gauhar Rahman; Abdel-Haleem Abdel-Aty; Emad E. Mahmoud; Kottakkaran Sooppy Nisar

doi:10.3934/math.2021266

AIMS Mathematics

2021, Volume 6, Issue 5: 4492-4506. doi: 10.3934/math.2021266

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Research article

Estimation of generalized fractional integral operators with nonsingular function as a kernel

1.
Department of Mathematics, University of Lahore, Lahore, Pakistan
2.
Department of Mathematics, University of Sargodha, Sargodha, Pakistan
3.
Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan
4.
Department of Physics, College of Sciences, University of Bisha, P.O. Box 344, Bisha, 61922, Saudi Arabia
5.
Physics Department, Faculty of Science, Al-Azhar University, Assiut, 71524, Egypt
6.
Department of Mathematics and Statistics, College of Science, Taif University, PO Box 11099, Taif 21944, Saudi Arabia
7.
Department of Mathematics, College of Arts and Sciences, Wadi Aldawser, 11991, Prince Sattam bin Abdulaziz University, Saudi Arabia

Received: 23 November 2020 Accepted: 01 February 2021 Published: 22 February 2021
MSC : 11S80, 26A33, 33C10, 33C20

Bessel function has a significant role in fractional calculus having immense applications in physical and theoretical approach. Present work aims to introduce fractional integral operators in which generalized multi-index Bessel function as a kernel, and develop some important special cases which are connected with fractional operators in fractional calculus. Here, we construct important links to familiar findings from some individual occurrence with our key outcomes.
- beta function,
- fractional operators,
- generalized multi-index Bessel function,
- Wright's function
Citation: Iqra Nayab, Shahid Mubeen, Rana Safdar Ali, Gauhar Rahman, Abdel-Haleem Abdel-Aty, Emad E. Mahmoud, Kottakkaran Sooppy Nisar. Estimation of generalized fractional integral operators with nonsingular function as a kernel[J]. AIMS Mathematics, 2021, 6(5): 4492-4506. doi: 10.3934/math.2021266

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Abstract

Bessel function has a significant role in fractional calculus having immense applications in physical and theoretical approach. Present work aims to introduce fractional integral operators in which generalized multi-index Bessel function as a kernel, and develop some important special cases which are connected with fractional operators in fractional calculus. Here, we construct important links to familiar findings from some individual occurrence with our key outcomes.

References

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