International Journal of Nonlinear Analysis and Applications
Gr$\ddot{u}$ss type integral inequalities for a new class of $k$-fractional integrals
Document Type : Research Paper
Authors
1 Department of Mathematics, G.C. University Faisalabad, Faisalabad, Pakistan
2 Department of Mathematics, COMSATS University Islamabad, Attock Campus, Pakistan
3 Department of Mathematics, University of Sargodha, Sargodha, Pakistan
Abstract
The main aim of this research article is to present the generalized $k$-fractional conformable integrals and an improved version of Gr$\ddot{u}$ss integral inequality via the fractional conformable integral in status of a new parameter $k>0$. Here for establishing Gr$\ddot{u}$ss inequality in fractional calculus the classical method of proof has been adopted also related results with Gr$\ddot{u}$ss inequality have been discussed. This work contributes in the current research by providing mathematical results along with their verifications.
Keywords
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[26] Park, J., 2015. Some integral inequalities for convex functions via Riemann-Liouville integrals. Appl. Math. Sci. 9, 1341-1353.
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[35] Usta, F. and Sarkaya, M.Z., 2017. Explicit bounds on certain integral inequalities via conformable fractional calculus. Cogent Mathematics, 4:1277505.
[36] Usta, F., Budak, H., and Sarkaya, M.Z., 2017. On Chebychev type inequalities for fractional integral operators, AIP Conference Proceedings, 1833: 020045.
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Volume 12, Issue 1
May 2021Pages 541-554
- Receive Date: 28 May 2018
- Revise Date: 11 November 2019
- Accept Date: 06 February 2020
- First Publish Date: 06 February 2021