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Extended generalized Mittag-Leffler function applied on fractional integral inequalities

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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.

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.

참고문헌 (12)

  1. M. Andri´c, "A further extension of Mittag-Leffler function", Fract. Calc. Appl. Anal, 21(5), pp.1377~1395 (2018)[DOI]
  2. Muhammad Arshad, "A new extension of the Mittag-Leffler function", 대한수학회논문집, 33(2), pp.549~560 (2018), 대한수학회
  3. Z. Dahmani, "New classes of integral inequalities of fractional order", Matematiche(Catania), 69(1), pp.237~247 (2014)[DOI]
  4. A. A. Kilbas, "Theory and Applications of Fractional Differential Equations" (2006), Elsevier Science B.V.
  5. W. Liu, "Several interesting integral inequalities", J. Math. Inequal, 3(2), pp.201~212 (2009)[DOI]
  6. K. S. Nisar, "Fractional integrations of a generalized Mittag-Leffler type function and its application", Mathematics, 7(12), pp.1230~ (2019)[DOI]
  7. K. S. Nisar, "Fractional calculus operators with Appell function kernels applied to Srivastava polynomials and extended MittagLeffler function", Adv. Difference Equ., 2020, pp.148~161 (2020)[DOI]
  8. T. R. Prabhakar, "A singular integral equation with a generalized Mittag Leffler function in the kernel", Yokohama Math. J, 19, pp.7~15 (1971)
  9. G. Rahman, "The extended Mittag-Leffler function via fractional calculus", J. Nonlinear Sci. Appl, 10(8), pp.4244~4253 (2017)[DOI]
  10. T. O. Salim, "A generalization of Mittag-Leffler function and integral operator associated with fractional calculus", J. Fract. Calc. Appl, 3(5), pp.1~13 (2012)
  11. A. K. Shukla, "On a generalization of Mittag-Leffler function and its properties", J. Math. Anal. Appl, 336(2), pp.797~811 (2007)[DOI]
  12. H. M. Srivastava, "Fractional calculus with an integral operator containing a generalized Mittag-Leffler function in the kernel", Appl. Math. Comput, 211(1), pp.198~210 (2009)[DOI]

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