Generalized Minkowski-type Fractional Inequalities Involving Extended Mittag-leffler Function


Affiliations

  • University of Split, Faculty of Civil Engineering, Architecture and Geodesy, Split, 21000, Croatia
  • COMSATS University, Department of Mathematics, Islamabad, Pakistan
  • RUDN University, Moscow, 117198, Russian Federation

Abstract

In this paper the reverse fractional Minkowski integral inequality using extended Mittag-Leffler function with the corresponding fractional integral operator is proved, as well as several related Minkowskitype inequalities.

Keywords

Minkowski inequality, Mittag-Leffler function, fractional integral operator

Full Text:

References

B. Ahmed, A. Alsaedi, M. Kirane and B. T. Torebek, Hermite-Hadamard, HermiteHadamard-Fej´er, Dragomir-Agarwal and Pachpatte type inequalities for convex functions via new fractional integrals, J. Comp. Appl. Math., 353. (2019), 120 - 129.

M. Andri´c, G. Farid, S. Mehmood and J. Peˇcari´c, P´olya-Szeg¨o and Chebyshev types inequalities via an extended generalized Mittag-Leffler function, Math. Inequal. Appl., 22. (4)(2019), 1365 - 1377.

M. Andri´c, G. Farid and J. Peˇcari´c, A further extension of Mittag-Leffler function, Fract. Calc. Appl. Anal., 21. (4)(2018), 1377 - 1395.

L. Bougoffa, On Minkowski and Hardy integral inequalities, J. Inequal. Pure Appl. Math., 7. (2)(2006), Article 60.

V. L. Chinchane, New approach of Minkowski fractional inequalities using generalized k-fractional integral operator, J. Indian Math. Soc., 85. (1-2)(2018), 32 - 41.

G. Farid, J. Peˇcari´c and ˇZ. Tomovski, Opial-type inequalities for fractional integral operator involving Mittag-Leffler function, Fractional Differ. Calc., 5. (1)(2015), 93 106.

S. K. Ntouyas, P. Agarwal and J. Tariboon, On P´olya-Szeg¨o and Chebyshev types inequalities involving the Riemann-Liouville fractional integral operators, J. Math. Inequal., 10. (2)(2016), 491 - 504.

T. R. Prabhakar, A singular integral equation with a generalized Mittag-Leffler function in the kernel, Yokohama Math. J., 19. (1971), 7 - 15.

G. Rahman, D. Baleanu, M. A. Qurashi, S. D. Purohit, S. Mubeen and M. Arshad, The extended Mittag-Leffler function via fractional calculus, J. Nonlinear Sci. Appl., 10. (8)(2017), 4244–4253.

T. O. Salim and A. W. Faraj, A generalization of Mittag-Leffler function and integral operator associated with fractional calculus, J. Fract. Calc. Appl., 3. (5)(2012), 1 - 13.

E. Set, M ¨ Ozdemir and S. S. Dragomir, On the Hermite-Hadamard inequality and other integral inequalities involving two functions, J. Inequal. Appl., (2010), 2010: 148102.

A. K. Shukla and J. C. Prajapati, On a generalization of Mittag-Leffler function and its properties, J. Math. Anal. Appl., 336. (2007), 797 - 811.

J. Vanterler da C. Sousa and E. Capelas de Oliveira, The Minkowski’s inequality by means of a generalized fractional integral, AIMS Mathematics, 3. (1)(2018), 131 - 147.

H. M. Srivastava and ˇZ. Tomovski, Fractional calculus with an integral operator containing a generalized Mittag-Leffler function in the kernel, Appl. Math. Comput., 211. (1)(2009), 198 - 210.

B. Sroysang, More on reverses of Minkowski’s integral inequality, Math. Aeterna, 3. (7)(2013), 597 - 600.


Refbacks

  • There are currently no refbacks.