Numerical solution of the multi-term variable-order space fractional nonlinear partial differential equations

[摘要] A numerical approach for solving the multi-term variable-order space fractional nonlinear partial differential equations is proposed. The fractional derivatives are described in the Caputo sense. The numerical approach is based on generalized Laguerre polynomials and finite difference method. The proposed scheme transforms the main problem to a system of nonlinear algebraic equations. The nonlinear system is solved by using Newton’s method. The validity and the applicability of the proposed technique are shown by numerical examples.

[学科分类] 数学（综合）

[关键词] nonlinear multi-term fractional partial differential equation;the variable-order Caputo fractional derivative;finite difference method;Newton’s method;generalized Laguerre polynomials