IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v545y2020ics0378437119321181.html
   My bibliography  Save this article

Certain new models of the multi space-fractional Gardner equation

Author

Listed:
  • Alderremy, A.A.
  • Saad, Khaled M.
  • Agarwal, Praveen
  • Aly, Shaban
  • Jain, Shilpi

Abstract

In this paper, we study an accurate numerical method for solving the multi space-fractional Gardner equation (MSFGE) with the Caputo–Fabrizio (CF) and Atangana–Baleanu (AB) fractional derivatives where the space-fractional terms are under the sense of Caputo. To the best knowledge of the reader, we are first to use the spectral collocation method based on the third Chebyshev approximations to reduced the multi space-fractional Gardner equation to a system of ordinary differential equations by using the properties of Chebyshev polynomials and then solved them via the finite difference method (FDM). By computing the absolute errors we present the effectiveness and accuracy of the proposed methods. The present paper investigates the dynamics of Gardner Equation by considering two fractional operators that is the Caputo–Fabrizio and Atangana–Baleanu, this is entirely new idea by using the two operators on a Gardner equation. Our results prove that the given procedure is an easy and efficient tool to investigate the solution of nonlinear equations with local and non-local singular kernels.

Suggested Citation

  • Alderremy, A.A. & Saad, Khaled M. & Agarwal, Praveen & Aly, Shaban & Jain, Shilpi, 2020. "Certain new models of the multi space-fractional Gardner equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    • Handle: RePEc:eee:phsmap:v:545:y:2020:i:c:s0378437119321181
    DOI: 10.1016/j.physa.2019.123806
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437119321181
    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.2019.123806?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. Defever, Fabrice & Reyes, José-Daniel & Riaño, Alejandro & Varela, Gonzalo, 2020. "All these worlds are yours, except india: The effectiveness of cash subsidies to export in nepal," European Economic Review, Elsevier, vol. 128(C).
    2. Kapetanios, George & Price, Simon & Tasiou, Menelaos & Ventouri, Alexia, 2021. "State-level wage Phillips curves," Econometrics and Statistics, Elsevier, vol. 18(C), pages 1-11.
    3. Emara, Noha & El Said, Ayah & Pearlman, Joseph, 2019. "On the Impact of Financial Inclusion on Financial Stability and Inequality: The Role of Macroprudential Policies," MPRA Paper 99258, University Library of Munich, Germany.
    4. Bai, Ye & Girma, Sourafel & Riaño, Alejandro, 2024. "Corporate acquisitions and firm-level uncertainty: Domestic versus cross-border deals," Journal of International Money and Finance, Elsevier, vol. 140(C).
    5. Che, X. & Katayama, H. & Lee, P., 2020. "Willingness to Pay for Brand Reputation: Lessons from the Volkswagen Diesel Emissions Scandal," Working Papers 20/02, Department of Economics, City University London.
    6. Laliotis, Ioannis & Minos, Dimitrios, 2020. "Spreading the disease: The role of culture," SocArXiv z4ndc, Center for Open Science.
    7. Aligishiev, Z. & Ben-Gad, M. & Pearlman, J., 2020. "Evaluating Historical Episodes using Shock Decompositions in the DSGE Model," Working Papers 20/10, Department of Economics, City University London.
    8. Bharadwaj, P. & Doiron, D. & Fiebig, D. G. & Suziedelyte, A., 2020. "Psychological Costs of Migration: Home Country Natural Disasters and Mental Health," Working Papers 20/03, Department of Economics, City University London.
    9. Offiaeli, K. & Yaman, F., 2020. "Social Norms as a Cost-Effective Measure of Managing Transport Demand: Evidence from an Experiment on the London Underground," Working Papers 20/07, Department of Economics, City University London.
    10. Che, X. & Huang, Y. & Zhang, L., 2020. "Supervisory Efficiency and Collusion in a Multiple-Agent Hierarchy," Working Papers 20/01, Department of Economics, City University London.
    11. Saad, Khaled M. & Gómez-Aguilar, J.F., 2018. "Analysis of reaction–diffusion system via a new fractional derivative with non-singular kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 703-716.
    12. Morales-Delgado, V.F. & Gómez-Aguilar, J.F. & Saad, Khaled M. & Khan, Muhammad Altaf & Agarwal, P., 2019. "Analytic solution for oxygen diffusion from capillary to tissues involving external force effects: A fractional calculus approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 48-65.
    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. Laila F. Seddek & Abdelhalim Ebaid & Essam R. El-Zahar & Mona D. Aljoufi, 2023. "Exact Solution of Non-Homogeneous Fractional Differential System Containing 2 n Periodic Terms under Physical Conditions," Mathematics, MDPI, vol. 11(15), pages 1-12, July.
    2. Ragwa S. E. Alatwi & Abdulrahman F. Aljohani & Abdelhalim Ebaid & Hind K. Al-Jeaid, 2022. "Two Analytical Techniques for Fractional Differential Equations with Harmonic Terms via the Riemann–Liouville Definition," Mathematics, MDPI, vol. 10(23), pages 1-11, 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. Coma, Julià & Chàfer, Marta & Pérez, Gabriel & Cabeza, Luisa F., 2020. "How internal heat loads of buildings affect the effectiveness of vertical greenery systems? An experimental study," Renewable Energy, Elsevier, vol. 151(C), pages 919-930.
    2. Rotundo, G. & Ausloos, M., 2007. "Microeconomic co-evolution model for financial technical analysis signals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 373(C), pages 569-585.
    3. Nie, Binjian & Zou, Boyang & She, Xiaohui & Zhang, Tongtong & Li, Yongliang & Ding, Yulong, 2020. "Development of a heat transfer coefficient based design method of a thermal energy storage device for transport air-conditioning applications," Energy, Elsevier, vol. 196(C).
    4. Li, Zhiyu & Xu, Xiwei & Jiang, Enchen & Han, Ping & Sun, Yan & Zhou, Ling & Zhong, Peidong & Fan, Xudong, 2020. "Alkane from hydrodeoxygenation (HDO) combined with in-situ multistage condensation of biomass continuous pyrolysis bio-oil via mixed supports catalyst Ni/HZSM-5-γ-Al2O3," Renewable Energy, Elsevier, vol. 149(C), pages 535-548.
    5. Zhu, H.B. & Zhou, Y.J. & Wu, W.J., 2020. "Modeling traffic flow mixed with automated vehicles considering drivers ’ character difference," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).
    6. Yoo, Yeawon & Escobedo, Adolfo R. & Skolfield, J. Kyle, 2020. "A new correlation coefficient for comparing and aggregating non-strict and incomplete rankings," European Journal of Operational Research, Elsevier, vol. 285(3), pages 1025-1041.
    7. Shi, Xin & Jiang, Haizhou & Li, Huan & Xu, Dong, 2020. "Maritime cluster research: Evolutionary classification and future development," Transportation Research Part A: Policy and Practice, Elsevier, vol. 133(C), pages 237-254.
    8. Saad, Khaled M. & Gómez-Aguilar, J.F. & Almadiy, Abdulrhman A., 2020. "A fractional numerical study on a chronic hepatitis C virus infection model with immune response," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    9. 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).
    10. Stjepan Srhoj & Vanja Vitezic & Joachim Wagner, 2020. "Export boosting policies and firm behaviour: Review of empirical evidence around the world," Working Paper Series in Economics 395, University of Lüneburg, Institute of Economics.
    11. El-Shagi, Makram & Tochkov, Kiril, 2024. "Regional heterogeneity and the provincial Phillips curve in China," Economic Analysis and Policy, Elsevier, vol. 81(C), pages 1036-1044.
    12. El-Dessoky Ahmed, M.M. & Altaf Khan, Muhammad, 2020. "Modeling and analysis of the polluted lakes system with various fractional approaches," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    13. Defever, F. & Riaño, A. & Varela, G., 2020. "Evaluating the Impact of Export Finance Support On Firm-level Export Performance: Evidence from Pakistan," Working Papers 20/14, Department of Economics, City University London.
    14. Ainoa Aparicio & Shoshana Grossbard, 2021. "Are COVID fatalities in the US higher than in the EU, and if so, why?," Review of Economics of the Household, Springer, vol. 19(2), pages 307-326, June.
    15. Suwan, Iyad & Abdeljawad, Thabet & Jarad, Fahd, 2018. "Monotonicity analysis for nabla h-discrete fractional Atangana–Baleanu differences," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 50-59.
    16. Aparicio Fenoll, Ainoa & Grossbard, Shoshana, 2020. "Intergenerational residence patterns and Covid-19 fatalities in the EU and the US," Economics & Human Biology, Elsevier, vol. 39(C).
    17. Yuping Deng & Yanrui Wu & Helian Xu, 2022. "Emission Reduction and Value-added Export Nexus at Firm Level," Economics Discussion / Working Papers 22-19, The University of Western Australia, Department of Economics.
    18. Agahi, Hamzeh & Khalili, Monavar, 2020. "Truncated Mittag-Leffler distribution and superstatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    19. Sharma, Rishi R., 2023. "An anatomy of Nepal’s remarkable export decline: A note," Journal of Asian Economics, Elsevier, vol. 89(C).
    20. Noha Emara & Mahmoud Mohieldin, 2020. "Financial inclusion and extreme poverty in the MENA region: a gap analysis approach," Review of Economics and Political Science, Emerald Group Publishing Limited, vol. 5(3), pages 207-230, July.

    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:545:y:2020:i:c:s0378437119321181. 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.