A DRBEM Formulation for a Fractional Dual-Phase-Lag Bioheat Model With Nanoparticle Photothermal Coupling

This paper presents a mathematical and computational framework for a coupled fractional dual-phase-lag (FDPL) bioheat model describing nanoparticle-enhanced photothermal processes with thermally activated drug transport. The governing system consists of nonlinear fractional partial differential equations incorporating Caputo time derivatives to capture thermal memory effects and finite-speed heat propagation. The model integrates optical absorption, nanoparticle transport, temperature-dependent drug release, and Arrhenius-type thermal damage within a unified formulation. To efficiently solve the resulting system, a dual reciprocity boundary element method (DRBEM) is developed, transforming the governing equations into a sequence of boundary-only integral problems. Fractional temporal terms are discretized using the L1 scheme, while nonlinear coupling is treated via an iterative procedure. The proposed method significantly reduces computational complexity by avoiding volumetric discretization while preserving accuracy. The numerical scheme is validated against analytical fractional benchmarks and systematic convergence studies, demonstrating first-order temporal and second-order spatial accuracy. Additional simulations illustrate the influence of fractional order, nanoparticle concentration, and perfusion on temperature evolution and damage formation. The results confirm that the proposed framework provides an accurate and efficient approach for solving nonlinear fractional PDE systems arising in coupled heat transfer and transport phenomena.