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This paper provides a new numerical strategy to solve fractional in spacereaction-diffusion equations on bounded domains under homogeneous Dirichletboundary conditions. Using the matrix transform method the fractional Laplacianoperator is replaced by a matrix which, in general, is dense. The approach herepresented is based on the approximation of this matrix by the product of twosuitable banded matrices. This leads to a semi-linear initial value problem inwhich the matrices involved are sparse. Numerical results are presented toverify the effectiveness of the proposed solution strategy.

Rational approximation to the fractional Laplacian operator in reaction-diffusion problems