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EXTENDED GENERALIZED MITTAG-LEFFLER FUNCTION APPLIED ON FRACTIONAL INTEGRAL INEQUALITIES

  • Received : 2020.02.27
  • Accepted : 2020.06.26
  • Published : 2020.10.31

Abstract

This paper presents several fractional generalizations and extensions of known integral inequalities. To obtain these, an extended generalized Mittag-Leffler function and its fractional integral operator are used.

Keywords

References

  1. M. Andric, G. Farid, and J. Pecaric, A further extension of Mittag-Leffler function, Fract. Calc. Appl. Anal. 21 (2018), no. 5, 1377-1395. https://doi.org/10.1515/fca-2018-0072
  2. M. Arshad, J. Choi, S. Mubeen, K. S. Nisar, and G. Rahman, A new extension of the Mittag-Leffler function, Commun. Korean Math. Soc. 33 (2018), no. 2, 549-560. https://doi.org/10.4134/CKMS.c170216
  3. Z. Dahmani, New classes of integral inequalities of fractional order, Matematiche (Catania) 69 (2014), no. 1, 237-247. https://doi.org/10.4418/2014.69.1.18
  4. A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, 204, Elsevier Science B.V., Amsterdam, 2006.
  5. W. Liu, Q.-A. Ngo, and V. N. Huy, Several interesting integral inequalities, J. Math. Inequal. 3 (2009), no. 2, 201-212. https://doi.org/10.7153/jmi-03-20
  6. K. S. Nisar, Fractional integrations of a generalized Mittag-Leffler type function and its application, Mathematics 7 (2019), no. 12, 1230. https://doi.org/10.3390/math7121230
  7. K. S. Nisar, D. L. Suthar, R. Agarwal, and S. D. Purohit, Fractional calculus operators with Appell function kernels applied to Srivastava polynomials and extended Mittag-Leffler function, Adv. Difference Equ. 2020 (2020), Paper No. 148, 14 pp. https://doi.org/10.1186/s13662-020-02610-3
  8. T. R. Prabhakar, A singular integral equation with a generalized Mittag Leffler function in the kernel, Yokohama Math. J. 19 (1971), 7-15.
  9. G. Rahman, D. Baleanu, M. Al Qurashi, S. D. Purohit, S. Mubeen, and M. Arshad, The extended Mittag-Leffler function via fractional calculus, J. Nonlinear Sci. Appl. 10 (2017), no. 8, 4244-4253. https://doi.org/10.22436/jnsa.010.08.19
  10. 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 (2012), no. 5, 1-13. https://doi.org/10.1142/9789814355216_0001
  11. A. K. Shukla and J. C. Prajapati, On a generalization of Mittag-Leffler function and its properties, J. Math. Anal. Appl. 336 (2007), no. 2, 797-811. https://doi.org/10.1016/j.jmaa.2007.03.018
  12. H. M. Srivastava and Tomovski, Fractional calculus with an integral operator containing a generalized Mittag-Leffler function in the kernel, Appl. Math. Comput. 211 (2009), no. 1, 198-210. https://doi.org/10.1016/j.amc.2009.01.055