Operational Matrix Method for the Variable Order Time Fractional Diffusion Equation Using Legendre Polynomials Approximation.

In this paper, a numerical method based on Legendre polynomials is proposed for solving the variable order time fractional diffusion equation. We adopt the Coimbra variable order time fractional operator, which can be viewed as a Caputo-type definition. Operational matrix of differentiation is also introduced. Combining this matrix with the properties of Legendre polynomials, we transform the initial problem into a Sylvester equation. Numerical example is provided to demonstrate the validity and applicability of the technique. Moreover, comparing the methodology with the known method shows that our approach is more efficient and more convenient. [ABSTRACT FROM AUTHOR]