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A space-time spectral approximation for solving nonlinear variable-order fractional sine and Klein-Gordon differential equations. (English) Zbl 1413.65382

Summary: In this paper, we propose an efficient spectral numerical method for solving sine and Klein-Gordon nonlinear variable-order fractional differential equations with the initial and Dirichlet boundary conditions. The approach is based on the shifted Legendre-Gauss and Chebyshev-Gauss collocation methods. The Caputo fractional derivative of variable order is adopted, and the original problems are reduced to systems of algebraic equations. The validity and effectiveness of the method is demonstrated by means of several numerical examples.

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
26A33 Fractional derivatives and integrals
35R11 Fractional partial differential equations
35Q53 KdV equations (Korteweg-de Vries equations)

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