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Certain new models of the multi space-fractional Gardner equation

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  • 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
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    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, Y. & Girma, S. & Riaño, A., 2020. "Corporate Acquisitions and Firm-level Uncertainty: Domestic versus Cross-Border Deals," Working Papers 20/09, Department of Economics, City University London.
    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.
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    Cited by:

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    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.

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