The Numerical Approximation of the Bioheat Equation of Space-Fractional Type Using Shifted Fractional Legendre Polynomials

Abstract

The aim of this paper is to employ the fractional shifted Legendre polynomials (FSLPs) in the matrix form to approximate the fractional derivatives and find the numerical solutions of the one-dimensional space-fractional bioheat equation (SFBHE). The Caputo formula was utilized to approximate the fractional derivative. The proposed methodology applied for two examples showed its usefulness and efficiency. The numerical results showed that the utilized technique is very efficacious with high accuracy and good convergence.