Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

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


Affiliations
1 Architecture and Geodesy, University of Split, Matice hrvatske 15, 21000 Split, Croatia
2 Department of Mathematics, COMSATS University, Islamabad, Attock Campus, Pakistan
3 RUDN University, Miklukho-Maklaya str. 6, 117198 Moscow, Russian Federation
     

   Subscribe/Renew Journal


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
Subscription Login to verify subscription
User
Notifications
Font Size


  • 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. Pecaric, Polya-Szego 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. Pecaric, 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 Z. Tomovski, ˇ 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 Z. Tomovski, ˇ 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.

Abstract Views: 574

PDF Views: 1




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

Abstract Views: 574  |  PDF Views: 1

Authors

Maja Andrić
Architecture and Geodesy, University of Split, Matice hrvatske 15, 21000 Split, Croatia
Ghulam Farid
Department of Mathematics, COMSATS University, Islamabad, Attock Campus, Pakistan
Josip Pećarić
RUDN University, Miklukho-Maklaya str. 6, 117198 Moscow, Russian Federation
Usama Siddique
Department of Mathematics, COMSATS University, Islamabad, Attock Campus, Pakistan

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

References





DOI: https://doi.org/10.18311/jims%2F2020%2F24607