Abstract
A new integral identity using the concepts of k-conformable fractional calculus is obtained. Utilizing the preinvexity property of the functions associated upper bounds is also obtained. Some special cases of the obtained results are also discussed.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
T. Abdeljawad, On conformable fractional calculus. J. Comput. Appl. Math. 279, 57–66 (2015)
B.D. Craven, Duality for generalized convex fractional programs, in Generalized Convexity in Optimization and Economics, ed. by S. Schaible, T. Ziemba (Academic, 1981), pp. 473–489
R. Diaz, E. Pariguan, On hypergeometric functions and k-pochhammer symbol. Divulg. Mat. 15(2), 179–192 (2007)
S.S. Dragomir, C.E.M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University (2000)
T.S. Du, J.G. Liao, L.Z. Chen, et al., Properties and RiemannLiouville fractional Hermite-Hadamard inequalities for the generalized (α, m)-preinvex functions. J. Inequal. Appl. 2016, 306 (2016)
M.A. Hanson, On sufficiency of the Kuhn-Tucker conditions. J. Math. Anal. Appl. 80, 545–550 (1981)
F. Jarad, E. Ugurlu, T. Abdeljawad, D. Baleanu, On a new class of fractional operators. Adv. Diff. Equ. 2017, 247 (2017)
R. Khalil, M.A. Horani, A. Yousef, M. Sababheh, A new definition of fractional derivative. J. Comput. Appl. Math. 264, 65–70 (2014)
A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204 (North-Holland, London/New York) (2006)
S. Mititelu, Invex sets. Stud. Cerc. Mat. 46(5), 529–532 (1994)
M.A. Noor, Hermite-Hadamard integral inequalities for \(\log \)-preinvex functions. J. Math. Anal. Approx. Theory 2, 126–131 (2007)
M.A. Noor, K.I. Noor, M.U. Awan, J. Li, On Hermite-Hadamard inequalities for h-preinvex functions. Filomat 28(7), 1463–1474 (2014)
C. Peng, C. Zhou, T.S. Du, RiemannLiouville fractional Simpson’s inequalities through generalized (m, h 1, h 2)- preinvexity. Ital. J. Pure Appl. Math. 38, 345–367 (2017)
F. Qi, S. Habib, S. Mubeen, M.N. Naeem, Generalized k-fractional conformable integrals and related inequalities. AIMS Math. 4(3), 343–358 (2019)
E. Set, A. Gozpinar, S.I. Butt, A study on HermiteHadamard-type inequalities via new fractional conformable integrals. Asian-Euorpian J. Math. (2019, Accepted)
M.Z. Sarikaya, A. Karaca, On the k-Riemann-Liouville fractional integral and applications. Int. J. Stat. Math. 1(3), 33–43 (2014)
M.Z. Sarikaya, E. Set, H. Yaldiz, N. Basak, Hermite-Hadamard’s inequalities for fractional integrals and related fractional inequalities. Math. Comput. Model. 57, 2403–2407 (2013)
S. Wu, M.U. Awan, M.V. Mihai, M.A. Noor, S. Talib, Estimates of upper bound for a kth order differentiable functions involving Riemann-Liouville integrals via higher order strongly h-preinvex functions. J. Inequal. Appl. 2019, 227 (2019)
T. Weir, B. Mond, Preinvex functions in multiple objective optimization. J. Math. Anal. Appl. 136, 29–38 (1988)
Acknowledgements
This research is supported by the HEC NRPU project No: 8081/Punjab/NRPU/R&D/HEC/2017.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Awan, M.U., Noor, M.A., Talib, S., Noor, K.I., Rassias, T.M. (2021). New k-Conformable Fractional Integral Inequalities. In: Rassias, T.M. (eds) Approximation Theory and Analytic Inequalities . Springer, Cham. https://doi.org/10.1007/978-3-030-60622-0_3
Download citation
DOI: https://doi.org/10.1007/978-3-030-60622-0_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-60621-3
Online ISBN: 978-3-030-60622-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)