Some new integral inequalities for \(k\)-fractional integrals

Downloads

DOI:

https://doi.org/10.26637/mjm401/013

Abstract

The aim of the present paper is to investigate some new integral inequalities for \(k\)-fractional integrals. Moreover, special cases of the integral inequalities in this paper have been obtained by Tariboon et.al. in [22].

Keywords:

fractional integral inequalities, Grüss inequality, \(k\)-Reimann-Liouville calculus

Mathematics Subject Classification:

26A33, 26D10, 26D15
  • Jessada Tariboon Nonlinear Dynamic Analysis Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok, 10800 Thailand. https://orcid.org/0000-0001-8185-3539
  • Sotiris K. Ntouyas Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece.
  • Muharrem Tomar Department of Mathematics, Faculty of Science and Arts, Ordu University, 52200 Ordu, Turkey.
  • Pages: 100-110
  • Date Published: 01-01-2016
  • Vol. 4 No. 01 (2016): Malaya Journal of Matematik (MJM)

G.A. Anastassiou, M.R. Hooshmandasl, A. Ghasemi, F. Moftakharzadeh, Montgomery identities for fractional integrals and related fractional inequalities, J. Inequal. Pure Appl. Math. 10 (4) (2009), 1-6.

G.A. Anastassiou, Fractional Differentiation Inequalities, Springer Science, LLC, 2009. DOI: https://doi.org/10.1007/978-0-387-98128-4

S. Belarbi, Z. Dahmani, On some new fractional integral inequalities, J. Inequal. Pure Appl. Math. 10 (3) (2009), 1-12.

Z. Dahmani, New inequalities in fractional integrals, Int. J. Nonlinear Sci. 9 (4) (2010), 493-497.

Z. Dahmani, L. Tabharit, and S. Taf, New generalizations of Gruss inequality using Riemann-Liouville fractional integrals, Bull. Math. Anal. Appl. 2 (3) (2010), 93-99.

R. Diaz, and E. Pariguan, On hypergeometric functions and Pochhammer $k$-symbol, Divulg. Mat. 15 (2007), 179-192.

S.S. Dragomir, A generalization of Gruss inequality in inner product spaces and applications, J. Math. Anal. Appl. 237 (1999), 74-82. DOI: https://doi.org/10.1006/jmaa.1999.6452

S.S. Dragomir, Some integral inequalities of Grüss type, Indian J. Pure Appl. Math. 31 (4) 2002, 397-415.

N. Elezovic, L.J. Marangunic and J. Pecaric, Some improvements of Gruss type inequality, J.Math. Ineq. 1 (2007), 425-436. DOI: https://doi.org/10.7153/jmi-01-36

R. Gorenflo, F. Mainardi, Fractional calculus: integral and differential equations of fractional order, Springer Verlag, Wien, 1997. DOI: https://doi.org/10.1007/978-3-7091-2664-6_5

G. Grüss, Über das Maximum des absoluten Betrages von $frac{1}{b-a} int_a^b f(t) g(t) d t-frac{1}{(b-a)^2} int_a^b f(t) d t$ $cdot int_a^b g(t) d t$, Math. Z. $39(11)(1935), 215-226$. DOI: https://doi.org/10.1007/BF01201355

J. Hadamard, Essai sur l'etude des fonctions donnees par leur developpement de Taylor, J. Pure Appl. Math. $4(8) 1892,101-186$.

Latif, M. A. and Hussain, S., New inequalities of Ostrowski type for co-ordineted convex functions via fractional integrals, J. Fract. Calc Appl. 2 (9) (2012), 1-15.

X. Li, R. N. Mohapatra, R. S. Rodriguez, Gruss-type inequalities, J. Math. Anal. Appl. 267 (2002), 434-443. DOI: https://doi.org/10.1006/jmaa.2001.7565

U.N. Katugampola, New Approach Generalized Fractional Integral, Appl. Math. Comput. 218 (2011), 860865. DOI: https://doi.org/10.1016/j.amc.2011.03.062

K. S. Miller and B. Ross, An introduction to the fractional calculus and fractional differential equations, New York: Wiley, 1993.

S. Mubeen, and G. M. Habibullah, k-Fractional integrals and application, Internat. J. Contemporary Math. Sci. 7 (2012), 89-94.

B.G. Pachpatte, On multidimensional Grüss type inequalities, J. Inequal. Pure Appl. Math. 3 (2) Art. 27, 2002.

M.Z. Sarikaya, E. Set, H.Yaldiz, and N.Basak, Hermite -Hadamard's inequalities for fractional integrals and related fractional inequalities, Math. Comput. Modelling, 57 (2013), 2403-2407. DOI: https://doi.org/10.1016/j.mcm.2011.12.048

M. Z. Sarikaya and H. Yaldiz, On weighted Montogomery identities for Riemann-Liouville fractional integrals, Konuralp Journal of Mathematics, 1 (1) (2013), 48-53.

M.Z. Sarikaya and A. Karaca, On the $k$-Riemann-Liouville fractional integral and applications, Internati. J. Stat. Math. 1 (2) (2014), 33-43. DOI: https://doi.org/10.3724/SP.J.1087.2013.00035

J. Tariboon, S.K. Ntouyas and W. Sudsutad, Some new Riemann-Liouville fractional integral inequalities, Internat. J. Math. Math. Sci. Volume 2014, Article ID 869434, 6 pages. DOI: https://doi.org/10.1155/2014/869434

M. Tunc, On new inequalities for h-convex functions via Riemann-Liouville fractional integration, Filomat 27 (4) (2013), 559-565. DOI: https://doi.org/10.2298/FIL1304559T

G. Romero, L. Luque, G. Dorrego and R. Cerutti, On the $k$-Riemann-Liouville Fractional Derivative, Int. J. Contemp. Math. Sci. 8 (1) (2013), 41-51. DOI: https://doi.org/10.12988/ijcms.2013.13004

  • NA

Metrics

Metrics Loading ...

Published

01-01-2016

How to Cite

Jessada Tariboon, Sotiris K. Ntouyas, and Muharrem Tomar. “Some New Integral Inequalities for \(k\)-Fractional Integrals”. Malaya Journal of Matematik, vol. 4, no. 01, Jan. 2016, pp. 100-1, doi:10.26637/mjm401/013.