IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v172y2023ics0960077923004307.html
   My bibliography  Save this article

New fractal–fractional parametric inequalities with applications

Author

Listed:
  • Butt, Saad Ihsan
  • Khan, Ahmad

Abstract

In the present paper, we first establish a general parameterized identity for local fractional twice differentiable functions involving extended fractal–fractional integral operators. Thus by employing generalized convexity on differentiable mappings along with Yang’s Power-mean, Hölder’s and improved fractal integral inequalities lead us to develop variety of new fractal–fractional parameterized inequalities. Several examples are provided with graphical illustrations to prove the validity of new results. We give error analysis of improved bounds numerically and also by 2D, 3D graphical representations. Finally, we show that our main results recapture fractal variants of trapezoid, midpoint, Simpson and Bullen-type inequalities. Some related applications to the fractal means, moment of random variables and wave equations are given as well.

Suggested Citation

  • Butt, Saad Ihsan & Khan, Ahmad, 2023. "New fractal–fractional parametric inequalities with applications," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    • Handle: RePEc:eee:chsofr:v:172:y:2023:i:c:s0960077923004307
    DOI: 10.1016/j.chaos.2023.113529
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077923004307
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2023.113529?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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).
    2. 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).
    3. Huixia Mo & Xin Sui, 2014. "Generalized -Convex Functions on Fractal Sets," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-8, July.
    4. Ai-Min Yang & Xiao-Jun Yang & Zheng-Biao Li, 2013. "Local Fractional Series Expansion Method for Solving Wave and Diffusion Equations on Cantor Sets," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-5, June.
    5. 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).
    6. 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).
    7. 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.
    8. Wenbing Sun, 2021. "LOCAL FRACTIONAL OSTROWSKI-TYPE INEQUALITIES INVOLVING GENERALIZED h-CONVEX FUNCTIONS AND SOME APPLICATIONS FOR GENERALIZED MOMENTS," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(01), pages 1-12, February.
    9. Rasheed, T. & Butt, S.I. & Pečarić, Đ. & Pečarić, J., 2022. "Generalized cyclic Jensen and information inequalities," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    10. Chunyan Luo & Yuping Yu & Tingsong Du, 2021. "An Improvement Of Hã–Lder Integral Inequality On Fractal Sets And Some Related Simpson-Like Inequalities," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(05), pages 1-20, August.
    11. 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.
    12. 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.
    13. 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).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Du, Tingsong & Yuan, Xiaoman, 2023. "On the parameterized fractal integral inequalities and related applications," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    2. 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).
    3. 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).
    4. 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).
    5. 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.
    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. 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).
    8. 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).
    9. 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.
    10. 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).
    11. Khan, Dawood & Butt, Saad Ihsan, 2024. "Superquadraticity and its fractional perspective via center-radius cr-order relation," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    12. 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).
    13. Sayyari, Yamin & Dehghanian, Mehdi, 2024. "A new class of convex functions and applications in entropy and analysis," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    14. Neumann, Peter & Pastowski, Sven & Carpinelli, Sonia, 2024. "Bleisure Travel: Potenziale und Handlungsempfehlungen für die Tourismuspraxis," IU Discussion Papers - Hospitality, Tourism & Event 2 (August 2024), IU International University of Applied Sciences.
    15. 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.
    16. Ohud Almutairi & Adem Kılıçman, 2019. "Generalized Integral Inequalities for Hermite–Hadamard-Type Inequalities via s -Convexity on Fractal Sets," Mathematics, MDPI, vol. 7(11), pages 1-16, November.
    17. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Broca Index: A Simple Tool to Measure Ideal Body Weight," MPRA Paper 116852, University Library of Munich, Germany, revised 18 Jan 2023.
    18. 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).
    19. 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).
    20. Abdullah Ali H. Ahmadini & Waqar Afzal & Mujahid Abbas & Elkhateeb S. Aly, 2024. "Weighted Fejér, Hermite–Hadamard, and Trapezium-Type Inequalities for ( h 1 , h 2 ) –Godunova–Levin Preinvex Function with Applications and Two Open Problems," Mathematics, MDPI, vol. 12(3), pages 1-28, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:172:y:2023:i:c:s0960077923004307. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.