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New Hadamard-type integral inequalities via a general form of fractional integral operators

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  • Butt, Saad Ihsan
  • Yousaf, Saba
  • Akdemir, Ahmet Ocak
  • Dokuyucu, Mustafa Ali

Abstract

The main motivation in this article is to prove a new and general integral identity and to obtain new integral inequalities of various Hadamard types with the help of this identity. Some basic inequalities such as Hölder, Young, power-mean and Jensen inequality have been used to obtain inequalities, and it has been determined that the main findings are generalizations and repetitions of many results that exist in the literature. Another impressive aspect of the study is that a new version of the Atangana–Baleanu integral operator is used, which is a very useful integral operator. We have given some simulations to demonsrate the consistency and harmony of this interesting operator for different values of the parameters.

Suggested Citation

  • Butt, Saad Ihsan & Yousaf, Saba & Akdemir, Ahmet Ocak & Dokuyucu, Mustafa Ali, 2021. "New Hadamard-type integral inequalities via a general form of fractional integral operators," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    • Handle: RePEc:eee:chsofr:v:148:y:2021:i:c:s0960077921003799
    DOI: 10.1016/j.chaos.2021.111025
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    References listed on IDEAS

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    1. Michael Th. Rassias & Bicheng Yang, 2014. "A Multidimensional Hilbert-Type Integral Inequality Related to the Riemann Zeta Function," Springer Optimization and Its Applications, in: Nicholas J. Daras (ed.), Applications of Mathematics and Informatics in Science and Engineering, edition 127, pages 417-433, Springer.
    2. Bicheng Yang, 2014. "Multidimensional Hilbert-Type Integral Inequalities and Their Operators Expressions," Springer Optimization and Its Applications, in: Themistocles M. Rassias & László Tóth (ed.), Topics in Mathematical Analysis and Applications, edition 127, pages 769-814, Springer.
    3. 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.
    4. Kumar, Devendra & Singh, Jagdev & Baleanu, Dumitru & Sushila,, 2018. "Analysis of regularized long-wave equation associated with a new fractional operator with Mittag-Leffler type kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 155-167.
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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. Khan, Dawood & Butt, Saad Ihsan, 2024. "Superquadraticity and its fractional perspective via center-radius cr-order relation," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    3. Yu, Shuhong & Zhou, Yunxiu & Du, Tingsong, 2022. "Certain midpoint-type integral inequalities involving twice differentiable generalized convex mappings and applications in fractal domain," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    4. Butt, Saad Ihsan & Khan, Ahmad, 2023. "New fractal–fractional parametric inequalities with applications," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    5. Sayyari, Yamin & Dehghanian, Mehdi, 2024. "A new class of convex functions and applications in entropy and analysis," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    6. Peng, Yu & Özcan, Serap & Du, Tingsong, 2024. "Symmetrical Hermite–Hadamard type inequalities stemming from multiplicative fractional integrals," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    7. 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.

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