IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v481y2017icp276-283.html
   My bibliography  Save this article

A new fractional operator of variable order: Application in the description of anomalous diffusion

Author

Listed:
  • Yang, Xiao-Jun
  • Machado, J.A. Tenreiro

Abstract

In this paper, a new fractional operator of variable order with the use of the monotonic increasing function is proposed in sense of Caputo type. The properties in term of the Laplace and Fourier transforms are analyzed and the results for the anomalous diffusion equations of variable order are discussed. The new formulation is efficient in modeling a class of concentrations in the complex transport process.

Suggested Citation

  • Yang, Xiao-Jun & Machado, J.A. Tenreiro, 2017. "A new fractional operator of variable order: Application in the description of anomalous diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 481(C), pages 276-283.
    • Handle: RePEc:eee:phsmap:v:481:y:2017:i:c:p:276-283
    DOI: 10.1016/j.physa.2017.04.054
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437117303606
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2017.04.054?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. Sun, HongGuang & Chen, Wen & Chen, YangQuan, 2009. "Variable-order fractional differential operators in anomalous diffusion modeling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(21), pages 4586-4592.
    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. Souad Bensid Ahmed & Adel Ouannas & Mohammed Al Horani & Giuseppe Grassi, 2022. "The Discrete Fractional Variable-Order Tinkerbell Map: Chaos, 0–1 Test, and Entropy," Mathematics, MDPI, vol. 10(17), pages 1-13, September.
    2. Qu, Hai-Dong & Liu, Xuan & Lu, Xin & ur Rahman, Mati & She, Zi-Hang, 2022. "Neural network method for solving nonlinear fractional advection-diffusion equation with spatiotemporal variable-order," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    3. Ganji, R.M. & Jafari, H. & Baleanu, D., 2020. "A new approach for solving multi variable orders differential equations with Mittag–Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    4. Tabatabaei, S. Sepehr & Talebi, H.A. & Tavakoli, M., 2017. "A novel adaptive order/parameter identification method for variable order systems application in viscoelastic soft tissue modeling," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 447-455.
    5. Hamid, M. & Usman, M. & Haq, R.U. & Wang, W., 2020. "A Chelyshkov polynomial based algorithm to analyze the transport dynamics and anomalous diffusion in fractional model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    6. Zahra, Waheed K. & Abdel-Aty, Mahmoud & Abidou, Diaa, 2020. "A fractional model for estimating the hole geometry in the laser drilling process of thin metal sheets," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    7. Meng, Ruifan & Yin, Deshun & Yang, Haixia & Xiang, Guangjian, 2020. "Parameter study of variable order fractional model for the strain hardening behavior of glassy polymers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    8. Chang, Ailian & Sun, HongGuang & Zheng, Chunmiao & Lu, Bingqing & Lu, Chengpeng & Ma, Rui & Zhang, Yong, 2018. "A time fractional convection–diffusion equation to model gas transport through heterogeneous soil and gas reservoirs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 356-369.
    9. Wu, Fei & Gao, Renbo & Liu, Jie & Li, Cunbao, 2020. "New fractional variable-order creep model with short memory," Applied Mathematics and Computation, Elsevier, vol. 380(C).
    10. Li, Jun-Feng & Jahanshahi, Hadi & Kacar, Sezgin & Chu, Yu-Ming & Gómez-Aguilar, J.F. & Alotaibi, Naif D. & Alharbi, Khalid H., 2021. "On the variable-order fractional memristor oscillator: Data security applications and synchronization using a type-2 fuzzy disturbance observer-based robust control," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    11. Zhang, Jiali & Fang, Zhi-Wei & Sun, Hai-Wei, 2022. "Robust fast method for variable-order time-fractional diffusion equations without regularity assumptions of the true solutions," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    12. Zeid, Samaneh Soradi, 2019. "Approximation methods for solving fractional equations," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 171-193.
    13. Noureddine Djenina & Adel Ouannas & Iqbal M. Batiha & Giuseppe Grassi & Viet-Thanh Pham, 2020. "On the Stability of Linear Incommensurate Fractional-Order Difference Systems," Mathematics, MDPI, vol. 8(10), pages 1-12, October.
    14. Mian Bahadur Zada & Muhammad Sarwar & Thabet Abdeljawad & Aiman Mukheimer, 2021. "Coupled Fixed Point Results in Banach Spaces with Applications," Mathematics, MDPI, vol. 9(18), pages 1-12, September.
    15. Chauhan, Archana & Gautam, G.R. & Chauhan, S.P.S. & Dwivedi, Arpit, 2023. "A validation on concept of formula for variable order integral and derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    16. Eftekhari, Tahereh & Rashidinia, Jalil, 2022. "A novel and efficient operational matrix for solving nonlinear stochastic differential equations driven by multi-fractional Gaussian noise," Applied Mathematics and Computation, Elsevier, vol. 429(C).
    17. Hossein Fazli & HongGuang Sun & Juan J. Nieto, 2020. "Fractional Langevin Equation Involving Two Fractional Orders: Existence and Uniqueness Revisited," Mathematics, MDPI, vol. 8(5), pages 1-10, May.
    18. Guo, Gang & Li, Kun & Wang, Yuhui, 2015. "Exact solutions of a modified fractional diffusion equation in the finite and semi-infinite domains," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 417(C), pages 193-201.
    19. Li, Qiaoping & Liu, Sanyang & Chen, Yonggang, 2018. "Combination event-triggered adaptive networked synchronization communication for nonlinear uncertain fractional-order chaotic systems," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 521-535.
    20. Pu, Zhe & Ran, Maohua & Luo, Hong, 2021. "Fast and high-order difference schemes for the fourth-order fractional sub-diffusion equations with spatially variable coefficient under the first Dirichlet boundary conditions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 110-133.

    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:phsmap:v:481:y:2017:i:c:p:276-283. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.