A study of fractional order dual-phase-lag bioheat transfer model

In this study, we have established a space-time fractional DPL bioheat transfer model in the presence of temperature-dependent metabolic and space-time dependent electromagnetic heat sources. Applying the Legendre wavelet collocation method, the fractional order partial differential equation is reduced into the system of algebraic equations, which has been solved using the Newton iteration method. The error bound as well as stability analysis and numerical scheme validation are provided. The time to achieve for the position of hyperthermia is discussed in three cases: the DPL model, the time-fractional DPL model, and the space-time-fractional DPL model. The effect of variability of time and space fractional derivative orders (alpha and beta), transmitted power (P) and lagging times on the temperature profile in biological tissue at a different time are discussed in detail. We conclude that a suitable value of alpha, beta, tau(T), tau(q), and P provides a desirable temperature at a particular time in thermal therapies. Such knowledge will be very useful in the clinical therapeutic application.