IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v144y2021ics0960077921000308.html
   My bibliography  Save this article

Fractional aspects of coupled mass-spring system

Author

Listed:
  • Zafar, Zain Ul Abadin
  • Younas, Samina
  • Hussain, Muhammad Tanveer
  • Tunç, Cemil

Abstract

In this article, the non-integer equations of the coupled mass-spring system with Atangana Baleanu fractional derivatives is offered. The physical entities of the structure are well-preserved by presenting an supplementary stricture χ. A nonlinear model with damping factor is considered. The existence and uniqueness problem to related model are scanned by fixed point principle. Our consequences spectacle that the mechanical components reveal viscoelastic behaviors generating temporal fractality at diverse scales and exhibit the existence of material heterogeneities in the mechanical modules. The comparison Jajarmi predictor corrector and Caputo methods is also given.

Suggested Citation

  • Zafar, Zain Ul Abadin & Younas, Samina & Hussain, Muhammad Tanveer & Tunç, Cemil, 2021. "Fractional aspects of coupled mass-spring system," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    • Handle: RePEc:eee:chsofr:v:144:y:2021:i:c:s0960077921000308
    DOI: 10.1016/j.chaos.2021.110677
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921000308
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.110677?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. Allahviranloo, Tofigh & Ghanbari, Behzad, 2020. "On the fuzzy fractional differential equation with interval Atangana–Baleanu fractional derivative approach," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    2. Uçar, Sümeyra & Uçar, Esmehan & Özdemir, Necati & Hammouch, Zakia, 2019. "Mathematical analysis and numerical simulation for a smoking model with Atangana–Baleanu derivative," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 300-306.
    3. Atangana, Abdon & Koca, Ilknur, 2016. "Chaos in a simple nonlinear system with Atangana–Baleanu derivatives with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 447-454.
    4. Iqbal, Muhammad Kashif & Abbas, Muhammad & Wasim, Imtiaz, 2018. "New cubic B-spline approximation for solving third order Emden–Flower type equations," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 319-333.
    5. Ghanbari, Behzad & Gómez-Aguilar, J.F., 2018. "Modeling the dynamics of nutrient–phytoplankton–zooplankton system with variable-order fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 114-120.
    6. Salari, Amjad & Ghanbari, Behzad, 2019. "Existence and multiplicity for some boundary value problems involving Caputo and Atangana–Baleanu fractional derivatives: A variational approach," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 312-317.
    7. Sharma, Sunil Kumar & Kumar, Dinesh, 2020. "A numerical study of new fractional model for convective straight fin using fractional-order Legendre functions," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    8. Khalid, Nauman & Abbas, Muhammad & Iqbal, Muhammad Kashif, 2019. "Non-polynomial quintic spline for solving fourth-order fractional boundary value problems involving product terms," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 393-407.
    9. Gao, Wei & Ghanbari, Behzad & Baskonus, Haci Mehmet, 2019. "New numerical simulations for some real world problems with Atangana–Baleanu fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 34-43.
    10. Singh, Jagdev & Kumar, Devendra & Hammouch, Zakia & Atangana, Abdon, 2018. "A fractional epidemiological model for computer viruses pertaining to a new fractional derivative," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 504-515.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Khalid A. Alattas & Mai The Vu & Omid Mofid & Fayez F. M. El-Sousy & Abdullah K. Alanazi & Jan Awrejcewicz & Saleh Mobayen, 2022. "Adaptive Nonsingular Terminal Sliding Mode Control for Performance Improvement of Perturbed Nonlinear Systems," Mathematics, MDPI, vol. 10(7), pages 1-18, March.
    2. Tabatabaei, S. Sepehr & Dehghan, Mohammad Reza & Talebi, Heidar Ali, 2022. "Real-time prediction of soft tissue deformation; a non-integer order modeling scheme and a practical verification for the theoretical concept," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).

    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. Zafar, Zain Ul Abadin & Zaib, Sumera & Hussain, Muhammad Tanveer & Tunç, Cemil & Javeed, Shumaila, 2022. "Analysis and numerical simulation of tuberculosis model using different fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    2. Baleanu, Dumitru & Jajarmi, Amin & Mohammadi, Hakimeh & Rezapour, Shahram, 2020. "A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    3. Zafar, Zain Ul Abadin & Ali, Nigar & Baleanu, Dumitru, 2021. "Dynamics and numerical investigations of a fractional-order model of toxoplasmosis in the population of human and cats," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    4. Ravichandran, C. & Logeswari, K. & Panda, Sumati Kumari & Nisar, Kottakkaran Sooppy, 2020. "On new approach of fractional derivative by Mittag-Leffler kernel to neutral integro-differential systems with impulsive conditions," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    5. Ghanbari, Behzad & Djilali, Salih, 2020. "Mathematical analysis of a fractional-order predator-prey model with prey social behavior and infection developed in predator population," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    6. Saad, Khaled M. & Srivastava, H.M. & Gómez-Aguilar, J.F., 2020. "A Fractional Quadratic autocatalysis associated with chemical clock reactions involving linear inhibition," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    7. Deniz, Sinan, 2021. "Optimal perturbation iteration method for solving fractional FitzHugh-Nagumo equation," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    8. Sekerci, Yadigar & Ozarslan, Ramazan, 2020. "Respiration Effect on Plankton–Oxygen Dynamics in view of non-singular time fractional derivatives," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 553(C).
    9. Uçar, Sümeyra & Uçar, Esmehan & Özdemir, Necati & Hammouch, Zakia, 2019. "Mathematical analysis and numerical simulation for a smoking model with Atangana–Baleanu derivative," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 300-306.
    10. Owolabi, Kolade M., 2019. "Mathematical modelling and analysis of love dynamics: A fractional approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 849-865.
    11. Kumar, Ashish & Pandey, Dwijendra N., 2020. "Existence of mild solution of Atangana–Baleanu fractional differential equations with non-instantaneous impulses and with non-local conditions," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    12. Fetecau, C. & Zafar, A.A. & Vieru, D. & Awrejcewicz, J., 2020. "Hydromagnetic flow over a moving plate of second grade fluids with time fractional derivatives having non-singular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    13. Taneco-Hernández, M.A. & Morales-Delgado, V.F. & Gómez-Aguilar, J.F., 2019. "Fundamental solutions of the fractional Fresnel equation in the real half-line," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 807-827.
    14. Dineshkumar, C. & Udhayakumar, R. & Vijayakumar, V. & Nisar, Kottakkaran Sooppy & Shukla, Anurag, 2022. "A note concerning to approximate controllability of Atangana-Baleanu fractional neutral stochastic systems with infinite delay," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    15. Veeresha, P. & Baskonus, Haci Mehmet & Prakasha, D.G. & Gao, Wei & Yel, Gulnur, 2020. "Regarding new numerical solution of fractional Schistosomiasis disease arising in biological phenomena," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    16. Qureshi, Sania & Bonyah, Ebenezer & Shaikh, Asif Ali, 2019. "Classical and contemporary fractional operators for modeling diarrhea transmission dynamics under real statistical data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    17. Ghanbari, Behzad & Günerhan, Hatıra & Srivastava, H.M., 2020. "An application of the Atangana-Baleanu fractional derivative in mathematical biology: A three-species predator-prey model," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    18. Nguiwa, Tchule & Kolaye, Gabriel Guilsou & Justin, Mibaile & Moussa, Djaouda & Betchewe, Gambo & Mohamadou, Alidou, 2021. "Dynamic study of SIAISQVR−B fractional-order cholera model with control strategies in Cameroon Far North Region," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    19. Yavuz, Mehmet & Bonyah, Ebenezer, 2019. "New approaches to the fractional dynamics of schistosomiasis disease model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 373-393.
    20. Ravichandran, C. & Logeswari, K. & Jarad, Fahd, 2019. "New results on existence in the framework of Atangana–Baleanu derivative for fractional integro-differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 194-200.

    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:144:y:2021:i:c:s0960077921000308. 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.