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Numerical solution of the nonlinear conformable space–time fractional partial differential equations

Abstract

In this paper, a numerical approach for solving the nonlinear space-time fractional partial differential equations with variable coefficients is proposed. The fractional derivatives are described in the conformable sense. The numerical approach is based on shifted Chebyshev polynomials of the second kind and finite difference method. The proposed scheme reduces the main problem to a system of nonlinear algebraic equations. The validity and the applicability of the proposed technique are shown by numerical examples.

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Correspondence to H. Çerdik Yaslan.

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Communicated by G.D. Veerappa Gowda.

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Yaslan, H.Ç. Numerical solution of the nonlinear conformable space–time fractional partial differential equations. Indian J Pure Appl Math 52, 407–419 (2021). https://doi.org/10.1007/s13226-021-00057-0

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  • DOI: https://doi.org/10.1007/s13226-021-00057-0

Keywords

  • Nonlinear space–time fractional partial differential equation
  • Conformable fractional derivative
  • Finite difference method
  • Newton method
  • Shifted Chebyshev polynomials of the second kind

Mathematics Subject Classification

  • 35G31
  • 35R11
  • 65M70