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Yaslan, H. Çerdik

Numerical solution of the nonlinear conformable space-time fractional partial differential equations. (English) Zbl 07423837

Indian J. Pure Appl. Math. 52, No. 2, 407-419 (2021).
Summary: 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.

Cited in 1 Document

MSC:

65-XX Numerical analysis
35G31 Initial-boundary value problems for nonlinear higher-order PDEs
35R11 Fractional partial differential equations
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs

Keywords:

nonlinear spacetime fractional partial differential equation; conformable fractional derivative; finite difference method; Newton method; shifted Chebyshev polynomials of second kind
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\textit{H. Ç. Yaslan}, Indian J. Pure Appl. Math. 52, No. 2, 407--419 (2021; Zbl 07423837)
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