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Hermite–Hadamard inequalities for generalized σ−conformable integrals generated by co-ordinated functions

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  • Çi̇ri̇ş, Sümeyye Ermeydan
  • Yildirim, Hüseyin

Abstract

In this paper, we define generalized σ− conformable fractional integrals on co-ordinated functions and generalized σ−conformable fractional integrals for the functions of two variables. Furthermore, we obtain a new Hermite–Hadamard inequality by using the generalized Riemann–Liouville integrals by means of the generalized σ− conformable integral definition. Moreover, we demonstrate some consequences by utilizing Hermite–Hadamard inequality and by utilizing definitions which we define in the study. Additionally, we state and prove some inequalities.

Suggested Citation

  • Çi̇ri̇ş, Sümeyye Ermeydan & Yildirim, Hüseyin, 2024. "Hermite–Hadamard inequalities for generalized σ−conformable integrals generated by co-ordinated functions," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    • Handle: RePEc:eee:chsofr:v:181:y:2024:i:c:s0960077924001796
    DOI: 10.1016/j.chaos.2024.114628
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    References listed on IDEAS

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    1. 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.
    2. Du, Tingsong & Zhou, Taichun, 2022. "On the fractional double integral inclusion relations having exponential kernels via interval-valued co-ordinated convex mappings," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    3. Tingsong Du & Chunyan Luo & Zhijie Cao, 2021. "On The Bullen-Type Inequalities Via Generalized Fractional Integrals And Their Applications," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(07), pages 1-20, November.
    4. 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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