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Discrete almost maximal regularity and stability for fractional differential equations in Lp([0, 1], Ω)

Author

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  • Liu, Li
  • Fan, Zhenbin
  • Li, Gang
  • Piskarev, Sergey

Abstract

The present paper is devoted to the study of discrete almost maximal regularity and stability of the difference schemes of nonhomogeneous fractional evolution equations. Using the discretization method of the fractional derivative proposed by Ashyralyev, which actually is the same as the Grünwald-Letnikov approximation for the fractional derivative, the discrete almost maximal regularity and stability of the implicit difference scheme in Lτnp([0,1],Ωn) spaces are established. For the explicit difference scheme, the expression of the solution is obtained. Then the discrete almost maximal regularity and stability of the explicit difference scheme in Lτnp([0,1],Ωn) spaces are achieved as well.

Suggested Citation

  • Liu, Li & Fan, Zhenbin & Li, Gang & Piskarev, Sergey, 2021. "Discrete almost maximal regularity and stability for fractional differential equations in Lp([0, 1], Ω)," Applied Mathematics and Computation, Elsevier, vol. 389(C).
    • Handle: RePEc:eee:apmaco:v:389:y:2021:i:c:s0096300320305300
    DOI: 10.1016/j.amc.2020.125574
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    References listed on IDEAS

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    1. Allaberen Ashyralyev & Yasar Sozen & Pavel E. Sobolevskii, 2007. "A Note on the Parabolic Differential and Difference Equations," Abstract and Applied Analysis, Hindawi, vol. 2007, pages 1-16, April.
    2. Shouguo Zhu & Zhenbin Fan & Gang Li, 2017. "Optimal Controls for Riemann–Liouville Fractional Evolution Systems without Lipschitz Assumption," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 47-64, July.
    3. Roul, Pradip & Prasad Goura, V.M.K., 2020. "A high order numerical method and its convergence for time-fractional fourth order partial differential equations," Applied Mathematics and Computation, Elsevier, vol. 366(C).
    4. A. Ashyralyev & J. Pastor & S. Piskarev & H. A. Yurtsever, 2015. "Second Order Equations in Functional Spaces: Qualitative and Discrete Well-Posedness," Abstract and Applied Analysis, Hindawi, vol. 2015, pages 1-63, July.
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