Title: Some Norm Inequalities for Fractional Integral Operators
Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814
Article ID: MTJPAM-D-21-00016; Volume 4 / Issue 3 / Year 2022 (Special Issue), Pages 93-102
Document Type: Research Paper
Author(s): Jichang Kuang a
aDepartment of Mathematics, Hunan Normal University, Changsha, Hunan, 410081, P. R. China
Received: 10 January 2021, Accepted: 9 September 2021, Published: 7 November 2021.
Corresponding Author: Jichang Kuang (Email address: email@example.com)
Full Text: PDF
In this paper, we introduce some new fractional integral operators and fractional area balance operators in the Banach spaces. The corresponding norm inequalities are established. They are significant improvement and generalizations of many known and new classes of fractional integral operators.
Keywords: Norm inequality, Fractional integral operator, Fractional area balance operatorReferences:
- J. C. Kuang, Applied Inequalities, 5th Edition (in Chinese), Shangdong Science and Technology Press, Jinan, 2021.
- A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and applications of fractional differential equations, North-Holland Mathematics Studies, 204, Elsevier, New York, 2006.
- S. Mubeen and G. M. Habibullah, k-fractional integrals and applications, Int. J. Contemp. Math. Sci. 7, 89–94, 2012.
- S. Mubeen and S. Iqbal, Grüss type integral inequalities for generalized Riemann-Liouville k-fractional integrals, J. Inequal. Appl. 109, 2016.
- M. Z. Sarikaya, Z. Dahmani, M. E. Kiris and F. Ahmad, (k, s)-Riemann-Liouville fractional integral and applications, Hacet. J. Math. Stat. 45 (1), 77–89, 2016.
- E. Set, M. Tomar and M. Z. Sarkaya, On generalized Grüss type inequalities for k-fractional integrals, Appl. Math. Comp. 8 (269), 29–34, 2015.
- G. Abbas, K. Khuram Ali, G. Farid and A. Ur Rehman, Generalizations of some fractional integral inequalities via generalized Mittag-Leffer function, J. Inequal. Appl. 121, 2017.
- J. V. da Sousa and E. C. de Oliveira, On the ψ-Hilfer fractional derivative, Commun. Nonlinear Sci. Numer. Simul. 60, 72–91, 2018.
- Y. Zhao, H. Sang, W. Xiong and Z. Cui, Hermite-Hadamard type inequalities involving ψ-Riemann-Liouville fractional integrals via s-convex functions, J. Inequal. Appl. 128, 2020.
- S. S. Dragomir, Inequalities for the area balance of absolutely continuous functions, Stud. Univ. Babes-Bolyai Math. 63 (1), 37–57, 2018.
- J. U. Khan and M. A. Khan, Generalized conformable fractional integral operators, J. Comput. Appl. Math. 346, 378–389, 2019.
- S. Rashid, A. O. Akdemir, K. S. Nisar, T. Abdeljawad and G. Rahman, New generalized reverse Minkowski and related integral inequalities involving generalized fractional conformable integrals, J. Inequal. Appl. 177, 2020.
- B. Çelik, M. Ç. Gürbüz, M. E. Özdemir and E. Set, On integral inequalities related to the weighted and the extended Chebyshev functionls involving different fractional operators, J. Inequal. Appl. 246, 2020.
- I. Iscan, Jensen-Mercer inequality for GA-convex functions and some related inequalities, J. Inequal. Appl. 212, 2020.
- J. C. Kuang, Norm inequalities for generalized Laplace transforms, Editors: A. Raigorodskii, Th. M. Rassias, In: Trigonometric Sums and Their Applications, Springer, 2020.
- J. C. Kuang, Some new inequalities for fractional integral operators, Th. M. Rassias, Approximation and Computation in Science and Engineering, Springer, 2021.
- M. Z. Sarikaya, On the Hermite-Hadarmard-type inequalities for co-ordinated convex function via fractional integrals, Integral Transforms Spec. Funct. 25 (2), 134–147, 2014.
- S. Erden, H. Budak, M. Z. Sarikaya, S. Iftikhar and P. Kumam, Fractional Ostrowski type inequalities for bounded functions, J. Inequal. Appl. 123, 2020.
- S. Erden, H. Budak and M. Z. Sarikaya, Fractional Ostrowski type inequalities for functions of bounded variation with two variables, Miskolc Math. Notes 21 (1), 171–188, 2020.