Araştırma Makalesi

Some Fractal-Fractional Integral Inequalities for Different Kinds of Convex Functions

Cilt: 5 Sayı: ICOLES2021 Special Issue 30 Kasım 2022
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Some Fractal-Fractional Integral Inequalities for Different Kinds of Convex Functions

Öz

The main objective of this work is to establish new upper bounds for different kinds of convex functions by using fractal-fractional integral operators with power law kernel. Furthermore, to enhance the paper, some new inequalities are obtained for product of different kinds of convex functions. The analysis used in the proofs is fairly elementary and based on the use of the well known Hölder inequality.

Anahtar Kelimeler

Kaynakça

  1. [1] Samko S., Kilbas A., Marichev O., 1993. Fractional Integrals and Derivatives: Theory and Applications. Gordon and Breach, Linghorne.
  2. [2] Podlubny I., 1998. Fractional Differential Equations: An Introduction to Fractional Derivatives. Fractional Differential Equations to Methods of Their Applications vol. 198. Academic press.
  3. [3] Lazarević M. P., Rapaić M. R., BŠekara T., 2014. Introduction to Fractional Calculus with Brief Historical Background. Advanced Topics on Applications of Fractional Calculus on Control Problems, System Stability and Modeling, WSEAS Press.
  4. [4] Caputo M., Fabrizio M., 2015. A new definition of fractional derivative without singular kernel. Progress in Fractional Differentiation and Applications, 1(2), pp. 73-85.
  5. [5] Atangana A., Baleanu D., 2016. New fractional derivatives with non-local and non-singular kernel. Theory and Application to Heat Transfer Model, Thermal Science, 20(2), pp. 763-769.
  6. [6] Atangana A., 2017. Fractal-fractional differentiation and integration: connecting fractal calculus and fractional calculus to predict complex system. Chaos Soliton. Fract.,102, pp. 396-406.
  7. [7] Anderson G. D, Vamanamurthy M. K., Vuorinen M., 2007. Generalized convexity and inequalities, J. Math. Anal. Appl, 335, pp. 1294-1308.
  8. [8] Kirmaci U. S., Bakula M. K, Özdemir M. E., Pecaric J., 2007. Hadamard type inequalities of s-convex functions. Applied Mathematics and Computation, 193, pp. 26-35.

Ayrıntılar

Birincil Dil

İngilizce

Konular

Matematik

Bölüm

Araştırma Makalesi

Yayımlanma Tarihi

30 Kasım 2022

Gönderilme Tarihi

29 Aralık 2021

Kabul Tarihi

24 Şubat 2022

Yayımlandığı Sayı

Yıl 2022 Cilt: 5 Sayı: ICOLES2021 Special Issue

Kaynak Göster

APA
Yüksel, E. (2022). Some Fractal-Fractional Integral Inequalities for Different Kinds of Convex Functions. Kocaeli Journal of Science and Engineering, 5(ICOLES2021 Special Issue), 18-24. https://doi.org/10.34088/kojose.1050267
AMA
1.Yüksel E. Some Fractal-Fractional Integral Inequalities for Different Kinds of Convex Functions. KOJOSE. 2022;5(ICOLES2021 Special Issue):18-24. doi:10.34088/kojose.1050267
Chicago
Yüksel, Ebru. 2022. “Some Fractal-Fractional Integral Inequalities for Different Kinds of Convex Functions”. Kocaeli Journal of Science and Engineering 5 (ICOLES2021 Special Issue): 18-24. https://doi.org/10.34088/kojose.1050267.
EndNote
Yüksel E (01 Kasım 2022) Some Fractal-Fractional Integral Inequalities for Different Kinds of Convex Functions. Kocaeli Journal of Science and Engineering 5 ICOLES2021 Special Issue 18–24.
IEEE
[1]E. Yüksel, “Some Fractal-Fractional Integral Inequalities for Different Kinds of Convex Functions”, KOJOSE, c. 5, sy ICOLES2021 Special Issue, ss. 18–24, Kas. 2022, doi: 10.34088/kojose.1050267.
ISNAD
Yüksel, Ebru. “Some Fractal-Fractional Integral Inequalities for Different Kinds of Convex Functions”. Kocaeli Journal of Science and Engineering 5/ICOLES2021 Special Issue (01 Kasım 2022): 18-24. https://doi.org/10.34088/kojose.1050267.
JAMA
1.Yüksel E. Some Fractal-Fractional Integral Inequalities for Different Kinds of Convex Functions. KOJOSE. 2022;5:18–24.
MLA
Yüksel, Ebru. “Some Fractal-Fractional Integral Inequalities for Different Kinds of Convex Functions”. Kocaeli Journal of Science and Engineering, c. 5, sy ICOLES2021 Special Issue, Kasım 2022, ss. 18-24, doi:10.34088/kojose.1050267.
Vancouver
1.Ebru Yüksel. Some Fractal-Fractional Integral Inequalities for Different Kinds of Convex Functions. KOJOSE. 01 Kasım 2022;5(ICOLES2021 Special Issue):18-24. doi:10.34088/kojose.1050267

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