Fractional shifted legendre polynomials for solving timefractional bioheat equation

الملخص EN

The aims of this paper: to employ the fractional shifted Legendre polynomials (FSLPs) to approximate the fractional temporal derivatives by using definition Caputo formula for fractional differential operator.

The space derivatives of the order integers are approximated depending on the shifted Legendre polynomials.

The numerical tests suggest for two examples that the proposed approach are efficient and robust in its solutions for the time-fractional bioheat equation.

Furthermore, some the preliminaries and definitions of the fractional derivatives, theorems and lemmas related to the fractional shifted Legendre polynomials are inserted to verify the convergence results of the algorithm under consideration.

Finally, we discussed the error analysis.