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The main aim of this paper is to propose a new boundary element method (BEM) formulation for solving the nonlinear space-time fractional dual-phase-lag bio-heat transfer problems during electromagnetic radiation. Due to the advantages of BEM, such as not requiring a discretization of the interior of the treated region and providing a low RAM and CPU time. BEM is therefore a flexible and efficient tool for modeling bio-heat transfer problems. The efficiency of our proposed methodology has been improved by applying the communication-avoiding versions of the Arnoldi (CA-Arnoldi) preconditioner for solving the resulting linear systems arising from the BEM to reduce the iterations number and CPU time. Numerical results are depicted graphically to show the effects of time-fractional derivative order and space-fractional derivative order on the nonlinear temperature distributions. The numerical results also show the significant differences between the nonlinear temperature distributions of the classical Fourier, single-phase-lag, and dual-phase-lag bio-heat conduction models. To demonstrate the validity and accuracy of the proposed BEM methodology, numerical solutions for two-dimensional (2D) special case of the nonlinear space-time fractional dual phase lag bio-heat transfer problems are obtained and compared to experimental, Legendre wavelet collocation method (LWCM) and Fractional order Legendre functions and Galerkin method (FOLFs-GM).
Mohamed Abdelsabour Fahmy (Sun,) studied this question.