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

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.

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
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