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On the parameterized fractal integral inequalities and related applications

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  • Du, Tingsong
  • Yuan, Xiaoman

Abstract

The utilization of local fractional calculus to investigate inequalities has become a widespread research method, which has enriched the theory of inequalities. The current study, inspired by this methodology and combined with the parameterized approach, explores a series of novel inequalities in the fractal spaces. Firstly, a fractal Bullen-type inequality with one parameter is presented. Secondly, the integral identity involving two parameters is established in the fractal domains. As an effect of this outcome, we derive a series of parameterized inequalities related to local fractional differentiable functions that are generalized (s,P)-convex and generalized (s,P)-concave at absolute values, respectively. Several special cases are discussed in depth as well. Certain applications concerning the special means, the quadrature formulas and the probability density functions are delivered in the end.

Suggested Citation

  • Du, Tingsong & Yuan, Xiaoman, 2023. "On the parameterized fractal integral inequalities and related applications," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    • Handle: RePEc:eee:chsofr:v:170:y:2023:i:c:s096007792300276x
    DOI: 10.1016/j.chaos.2023.113375
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    1. Meftah, B. & Souahi, A. & Merad, M., 2022. "Some local fractional Maclaurin type inequalities for generalized convex functions and their applications," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    2. Luo, Chunyan & Wang, Hao & Du, Tingsong, 2020. "Fejér–Hermite–Hadamard type inequalities involving generalized h-convexity on fractal sets and their applications," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    3. Singh, Jagdev & Jassim, Hassan Kamil & Kumar, Devendra, 2020. "An efficient computational technique for local fractional Fokker Planck equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    4. Saad Ihsan Butt & Saba Yousaf & Hijaz Ahmad & Taher A. Nofal, 2022. "Jensen–Mercer Inequality And Related Results In The Fractal Sense With Applications," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(01), pages 1-11, February.
    5. Atangana, Abdon & Qureshi, Sania, 2019. "Modeling attractors of chaotic dynamical systems with fractal–fractional operators," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 320-337.
    6. Erden, Samet & Sarikaya, Mehmet Zeki, 2016. "Generalized Pompeiu type inequalities for local fractional integrals and its applications," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 282-291.
    7. Atangana, Abdon, 2020. "Modelling the spread of COVID-19 with new fractal-fractional operators: Can the lockdown save mankind before vaccination?," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    8. Rainier V. Sã Nchez C. & Jos㉠E. Sanabria & Eduard Trousselot, 2022. "NEW INEQUALITIES ON GENERALIZED m-CONVEXITY ON FRACTAL SETS," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(06), pages 1-17, September.
    9. Saad Ihsan Butt & Saba Yousaf & Muhammad Younas & Hijaz Ahmad & Shao-Wen Yao, 2022. "Fractal Hadamard–Mercer-Type Inequalities With Applications," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(02), pages 1-14, March.
    10. Hasan Kara & Hüseyin Budak & Fatih Hezenci, 2022. "New Extensions of the Parameterized Inequalities Based on Riemann–Liouville Fractional Integrals," Mathematics, MDPI, vol. 10(18), pages 1-12, September.
    11. Cheng, Qingjin & Luo, Chunyan, 2022. "Estimation of the parameterized integral inequalities involving generalized p-convex mappings on fractal sets and related applications," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    12. 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).
    13. 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).
    14. 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).
    15. 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).
    16. 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).
    17. Shuhong Yu & Pshtiwan Othman Mohammed & Lei Xu & Tingsong Du, 2022. "An Improvement Of The Power-Mean Integral Inequality In The Frame Of Fractal Space And Certain Related Midpoint-Type Integral Inequalities," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(04), pages 1-23, June.
    18. Wenbing Sun, 2021. "HERMITE–HADAMARD TYPE LOCAL FRACTIONAL INTEGRAL INEQUALITIES FOR GENERALIZED s-PREINVEX FUNCTIONS AND THEIR GENERALIZATION," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(04), pages 1-16, June.
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