A comprehensive Approach of Caputo Space Fractional Bioheat Model During Hyperthermia Based on Fractional Chebyshev Collocation Scheme

Abstract

This paper has found a numerical solution of the space fractional bioheat equation during the hyperthermia treatment. The space fractional derivative is used in the Caputo sense of order \((1<\mu \le 2)\). The finite difference method (FDM) and Chebyshev collocation method are implemented to find the numerical results. Shifted Chebyshev polynomials of the first kind and finite difference approximations with a particular choice of collocation points are used to reduce the given problem into a system of algebraic equations. The algorithm being used is stable and convergent. The results are explained by considering the different orders of space fractional derivatives. The numerical results are also described graphically in anomalous and standard form by taking different parameter values. The dimensionless values are used to find all the results. It is observed from the numerical results that the temperature increases as the fractional derivative decreases for the hyperthermia treatment.