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Numerical solutions of fuzzy fractional diffusion equations by an implicit finite difference scheme

Abstract

Fuzzy fractional diffusion equations are used to model certain phenomena in physics, hydrology biology and amongst others. In this paper, an implicit finite difference scheme is developed, analysed and applied to numerically solve a fuzzy time fractional diffusion equation. For our case, the fuzziness is in the coefficients as well as initial and boundary conditions. The time fractional derivative is defined using the Caputo formula. The stability of the implicit finite difference scheme is analysed by means of the Von Neumann method. A numerical example has been given to check the feasibility of the approach and to examine certain related aspects. It was found that the results obtained are in good agreement with the proposed theory. Hence, the proposed scheme is suitable for solving fuzzy time fractional diffusion equations.

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Correspondence to Hamzeh Zureigat.

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Zureigat, H., Ismail, A.I. & Sathasivam, S. Numerical solutions of fuzzy fractional diffusion equations by an implicit finite difference scheme. Neural Comput & Applic 31, 4085–4094 (2019). https://doi.org/10.1007/s00521-017-3299-7

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  • DOI: https://doi.org/10.1007/s00521-017-3299-7

Keywords

  • Fuzzy numbers
  • Caputo formula
  • Fuzzy time fractional diffusion equation
  • Implicit finite difference scheme