IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v438y2015icp81-93.html

Revisited Fisher’s equation in a new outlook: A fractional derivative approach

Author

Listed:
  • Alquran, Marwan
  • Al-Khaled, Kamel
  • Sardar, Tridip
  • Chattopadhyay, Joydev

Abstract

The well-known Fisher equation with fractional derivative is considered to provide some characteristics of memory embedded into the system. The modified model is analyzed both analytically and numerically. A comparatively new technique residual power series method is used for finding approximate solutions of the modified Fisher model. A new technique combining Sinc-collocation and finite difference method is used for numerical study. The abundance of the bird species Phalacrocorax carbois considered as a test bed to validate the model outcome using estimated parameters. We conjecture non-diffusive and diffusive fractional Fisher equation represents the same dynamics in the interval (memory index, α∈(0.8384,0.9986)). We also observe that when the value of memory index is close to zero, the solutions bifurcate and produce a wave-like pattern. We conclude that the survivability of the species increases for long range memory index. These findings are similar to Fisher observation and act in a similar fashion that advantageous genes do.

Suggested Citation

  • Alquran, Marwan & Al-Khaled, Kamel & Sardar, Tridip & Chattopadhyay, Joydev, 2015. "Revisited Fisher’s equation in a new outlook: A fractional derivative approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 438(C), pages 81-93.
    • Handle: RePEc:eee:phsmap:v:438:y:2015:i:c:p:81-93
    DOI: 10.1016/j.physa.2015.06.036
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437115005968
    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.2015.06.036?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

    for a different version of it.

    References listed on IDEAS

    as
    1. John Geweke, 1991. "Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments," Staff Report 148, Federal Reserve Bank of Minneapolis.
    2. Rana, Sourav & Bhattacharya, Sabyasachi & Pal, Joydeep & N’Guérékata, Gaston M. & Chattopadhyay, Joydev, 2013. "Paradox of enrichment: A fractional differential approach with memory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3610-3621.
    3. El-Ajou, Ahmad & Abu Arqub, Omar & Momani, Shaher & Baleanu, Dumitru & Alsaedi, Ahmed, 2015. "A novel expansion iterative method for solving linear partial differential equations of fractional order," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 119-133.
    4. Michael G. Neubert & Ingrid M. Parker, 2004. "Projecting Rates of Spread for Invasive Species," Risk Analysis, John Wiley & Sons, vol. 24(4), pages 817-831, August.
    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. Han, Yuxin & Huang, Xin & Gu, Wei & Zheng, Bolong, 2023. "Linearized transformed L1 finite element methods for semi-linear time-fractional parabolic problems," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    2. Zhao, Dazhi & Yu, Guozhu & Tian, Yan, 2020. "Recursive formulae for the analytic solution of the nonlinear spatial conformable fractional evolution equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    3. Atangana, Abdon, 2016. "On the new fractional derivative and application to nonlinear Fisher’s reaction–diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 948-956.
    4. Muhammed I. Syam, 2017. "A Numerical Solution of Fractional Lienard’s Equation by Using the Residual Power Series Method," Mathematics, MDPI, vol. 6(1), pages 1-9, December.

    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. Buddhavarapu, Prasad & Bansal, Prateek & Prozzi, Jorge A., 2021. "A new spatial count data model with time-varying parameters," Transportation Research Part B: Methodological, Elsevier, vol. 150(C), pages 566-586.
    2. Jesús Fernández-Villaverde & Juan F. Rubio-Ramirez, 2001. "Comparing dynamic equilibrium economies to data," FRB Atlanta Working Paper 2001-23, Federal Reserve Bank of Atlanta.
    3. Atahan Afsar; José Elías Gallegos; Richard Jaimes; Edgar Silgado Gómez & Jos� El�as Gallegos & Richard Jaimes & Edgar Silgado G�mez, 2020. "Reconciling Empirics and Theory: The Behavioral Hybrid New Keynesian Model," Vniversitas Económica, Universidad Javeriana - Bogotá, vol. 0(0), pages 1-41.
    4. Bai, Yizhou & Xue, Cheng, 2021. "An empirical study on the regulated Chinese agricultural commodity futures market based on skew Ornstein-Uhlenbeck model," Research in International Business and Finance, Elsevier, vol. 57(C).
    5. Mai Dao & Lam Nguyen, 2025. "Variable selection in macroeconomic stress test: a Bayesian quantile regression approach," Empirical Economics, Springer, vol. 68(3), pages 1113-1169, March.
    6. Michael T. Owyang, 2002. "Modeling Volcker as a non-absorbing state: agnostic identification of a Markov-switching VAR," Working Papers 2002-018, Federal Reserve Bank of St. Louis.
    7. Keane, Michael & Stavrunova, Olena, 2016. "Adverse selection, moral hazard and the demand for Medigap insurance," Journal of Econometrics, Elsevier, vol. 190(1), pages 62-78.
    8. González-Astudillo, Manuel, 2019. "An output gap measure for the euro area: Exploiting country-level and cross-sectional data heterogeneity," European Economic Review, Elsevier, vol. 120(C).
    9. Boeck, Maximilian & Feldkircher, Martin, 2021. "The Impact of Monetary Policy on Yield Curve Expectations," Journal of Economic Behavior & Organization, Elsevier, vol. 191(C), pages 887-901.
    10. Eiji Goto, 2020. "Industry Impacts of Unconventional Monetary Policy," 2020 Papers pgo873, Job Market Papers.
    11. Neha Choudhary & Abhishek Tyagi & Bhupendra Singh, 2022. "Analysing Load-Sharing System Model with Type-I and Type-II Failure Censored Data from Weibull Distribution," Annals of Data Science, Springer, vol. 9(4), pages 645-674, August.
    12. Shachat, Jason & Swarthout, J. Todd & Wei, Lijia, 2015. "A Hidden Markov Model For The Detection Of Pure And Mixed Strategy Play In Games," Econometric Theory, Cambridge University Press, vol. 31(4), pages 729-752, August.
    13. Houssa, Romain, 2013. "Uncertainty about welfare effects of consumption fluctuations," European Economic Review, Elsevier, vol. 59(C), pages 35-62.
    14. Tamás Krisztin & Philipp Piribauer, 2021. "A Bayesian spatial autoregressive logit model with an empirical application to European regional FDI flows," Empirical Economics, Springer, vol. 61(1), pages 231-257, July.
    15. Richardson, Robert & Kottas, Athanasios & Sansó, Bruno, 2017. "Flexible integro-difference equation modeling for spatio-temporal data," Computational Statistics & Data Analysis, Elsevier, vol. 109(C), pages 182-198.
    16. Chatterjee, Amar Nath & Ahmad, Bashir, 2021. "A fractional-order differential equation model of COVID-19 infection of epithelial cells," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    17. Joshua L. Warren & Melanie H. Chitwood & Benjamin Sobkowiak & Caroline Colijn & Ted Cohen, 2023. "Spatial modeling of Mycobacterium tuberculosis transmission with dyadic genetic relatedness data," Biometrics, The International Biometric Society, vol. 79(4), pages 3650-3663, December.
    18. Jiafang Song & Joshua L. Warren, 2022. "A Directionally Varying Change Points Model for Quantifying the Impact of a Point Source," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(1), pages 46-62, March.
    19. Abu Arqub, Omar & Al-Smadi, Mohammed, 2020. "An adaptive numerical approach for the solutions of fractional advection–diffusion and dispersion equations in singular case under Riesz’s derivative operator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    20. Amin Ghalamfarsa Mostofi & Mahmood Kharrati-Kopaei, 2025. "Nonparametric Bayesian inferences on the skewed data using a Dirichlet process mixture model," Statistical Papers, Springer, vol. 66(1), pages 1-24, January.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:438:y:2015:i:c:p:81-93. 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.