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Certain Simpson-type inequalities for twice-differentiable functions by conformable fractional integrals

Huseyin Budak|Fatih Hezenci
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2023.06|한국수학논문집 (Korean Journal of Mathematics)|제31권 제2호|pp. 217-228

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키워드

convex functionfractional calculusSimpson-type inequalityfractional conformable integrals
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초록

In this paper, an equality is established by twice-differentiable convex functions with respect to the conformable fractional integrals. Moreover, several Simpson-type inequalities are presented for the case of twice-differentiable convex functions via conformable fractional integrals by using the established equality. Furthermore, our results are provided by using special cases of obtained theorems.

Abstract

In this paper, an equality is established by twice-differentiable convex functions with respect to the conformable fractional integrals. Moreover, several Simpson-type inequalities are presented for the case of twice-differentiable convex functions via conformable fractional integrals by using the established equality. Furthermore, our results are provided by using special cases of obtained theorems.

참고문헌 (19)

  1. J. E. Pecaric, "Convex functions, partial orderings, and statistical applications" (1992), Academic Press, Inc
  2. M. Sarikaya, "On new inequalities of Simpson’s type for functions whose second derivatives absolute values are convex", Journal of Applied Mathematics, Statistics and Informatics, 9(1), pp.37~45 (2013)
  3. F. Hezenci, "New version of Fractional Simpson type inequalities for twice differentiable functions", Adv. Difference Equ, (460) (2021)
  4. M. Z. Sarikaya, "On the generalization of some integral inequalities and their applications", Mathematical and computer Modelling, 54(9-10), pp.2175~2182 (2011)
  5. D. Baleanu, "Fractional Calculus: Models and numerical methods" (2016), World Scientific
  6. G.A. Anastassiou, "Generalized fractional calculus: New advancements and applications" (2021), Springer
  7. N. Iqbal, "On Solutions of FractionalOrder Gas Dynamics Equation by Effective Techniques", J. Funct. Spaces Appl, 2022, pp.3341754~ (2022)
  8. N. Attia, "An efficient numerical technique for a biological population model of fractional order", Chaos, Solutions & Fractals, 141, pp.110349~ (2020)
  9. A. Gabr, "The Effect of the Parameters of the Generalized Fractional Derivatives On the Behavior of Linear Electrical Circuits", International Journal of Applied and Computational Mathematics, 7, pp.247~ (2021)
  10. R. Khalil, "A new definition of fractional derivative", J. Comput. Appl. Math, 264, pp.65~70 (2014)
  11. A. A. Abdelhakim, "The flaw in the conformable calculus : It is conformable because it is not fractional", Fract. Calc. Appl. Anal, 22, pp.242~254 (2019)
  12. D. Zhao, "General conformable fractional derivative and its physical interpretation", Calcolo, 54, pp.903~917 (2017)
  13. A. Hyder, "A new generalized θ-conformable calculus and its applications in mathematical physics", Phys. Scr, 96, pp.015208~ (2020)
  14. A. A. Kilbas, "Theory and Applications of Fractional Differential Equations", North-Holland Mathematics Studies, 204 (2006), Elsevier Sci. B.V
  15. F. Jarad, "On a new class of fractional operators", Adv. Difference Equ, 2017, pp.247~ (2017)
  16. X. You, "New Simpson type inequalities for twice differentiable functions via generalized fractional integrals", AIMS Mathematics, 7(3), pp.3959~3971 (2021)
  17. H. Budak, "On parameterized inequalities of Ostrowski and Simpson type for convex functions via generalized fractional integrals", Math. Methods Appl. Sci, 44(17), pp.12522~12536 (2021)
  18. H. Desalegn, "Simpson’s Type Inequalities for s-Convex Functions via Generalized Proportional Fractional Integral", Foundations, 2(3), pp.607~616 (2022)
  19. T. Abdeljawad, "On conformable fractional calculus", J. Comput. Appl. Math, 279, pp.57~66 (2015)

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