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New integral inequalities for differentiable convex functions via Atangana-Baleanu fractional integral operators

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  • Set, Erhan
  • Butt, Saad Ihsan
  • Akdemir, Ahmet Ocak
  • Karaoǧlan, Ali
  • Abdeljawad, Thabet

Abstract

Inequalities, including fractional integrals, have become a very popular method and have been the main motivation point for many studies in recent years. Studies have been carried out for many types of inequality, thereby introducing a new trend in inequality theory. In this study, new inequalities of Hermite-Hadamard type were obtained by using Atangana-Baleanu integral operators, which provide very useful and effective results with their use in fields such as fractional analysis, applied mathematics, mathematical biology and engineering. The fact that the main results were obtained for functions whose absolute value of the second derivative is convex. In the study, we have proved a new identity for twice differentiable convex functions and the modified version of the integral identity was given in the last section.

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  • Set, Erhan & Butt, Saad Ihsan & Akdemir, Ahmet Ocak & Karaoǧlan, Ali & Abdeljawad, Thabet, 2021. "New integral inequalities for differentiable convex functions via Atangana-Baleanu fractional integral operators," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    • Handle: RePEc:eee:chsofr:v:143:y:2021:i:c:s0960077920309450
    DOI: 10.1016/j.chaos.2020.110554
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    1. Jessada Tariboon & Sotiris K. Ntouyas & Weerawat Sudsutad, 2014. "Some New Riemann-Liouville Fractional Integral Inequalities," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2014, pages 1-6, March.
    2. Atangana, Abdon, 2018. "Non validity of index law in fractional calculus: A fractional differential operator with Markovian and non-Markovian properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 688-706.
    3. Atangana, Abdon & Gómez-Aguilar, J.F., 2018. "Fractional derivatives with no-index law property: Application to chaos and statistics," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 516-535.
    4. Ghanbari, Behzad & Atangana, Abdon, 2020. "A new application of fractional Atangana–Baleanu derivatives: Designing ABC-fractional masks in image processing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).
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    Cited by:

    1. Du, Tingsong & Yuan, Xiaoman, 2023. "On the parameterized fractal integral inequalities and related applications," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    2. Muhammad Bilal Khan & Eze R. Nwaeze & Cheng-Chi Lee & Hatim Ghazi Zaini & Der-Chyuan Lou & Khalil Hadi Hakami, 2023. "Weighted Fractional Hermite–Hadamard Integral Inequalities for up and down Ԓ-Convex Fuzzy Mappings over Coordinates," Mathematics, MDPI, vol. 11(24), pages 1-27, December.
    3. Almutairi, Ohud & Kiliçman, Adem, 2021. "Generalized Fejér–Hermite–Hadamard type via generalized (h−m)-convexity on fractal sets and applications," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    4. Butt, Saad Ihsan & Khan, Ahmad, 2023. "New fractal–fractional parametric inequalities with applications," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    5. Khan, Muhammad Bilal & Othman, Hakeem A. & Santos-García, Gustavo & Saeed, Tareq & Soliman, Mohamed S., 2023. "On fuzzy fractional integral operators having exponential kernels and related certain inequalities for exponential trigonometric convex fuzzy-number valued mappings," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    6. Abd-Allah Hyder & Areej A. Almoneef & Hüseyin Budak & Mohamed A. Barakat, 2022. "On New Fractional Version of Generalized Hermite-Hadamard Inequalities," Mathematics, MDPI, vol. 10(18), pages 1-15, September.
    7. Khan, Muhammad Bilal & Guirao, Juan L.G., 2023. "Riemann Liouville fractional-like integral operators, convex-like real-valued mappings and their applications over fuzzy domain," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    8. Peng, Yu & Özcan, Serap & Du, Tingsong, 2024. "Symmetrical Hermite–Hadamard type inequalities stemming from multiplicative fractional integrals," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    9. Asfand Fahad & Ayesha & Yuanheng Wang & Saad Ihsaan Butt, 2023. "Jensen–Mercer and Hermite–Hadamard–Mercer Type Inequalities for GA- h -Convex Functions and Its Subclasses with Applications," Mathematics, MDPI, vol. 11(2), pages 1-21, January.
    10. Yu, Yuping & Liu, Jun & Du, Tingsong, 2022. "Certain error bounds on the parameterized integral inequalities in the sense of fractal sets," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).

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