Fractional Mechanism with Power Law (Singular) and Exponential (Non-singular) Kernels and Its Applications in Bio Heat Transfer Model

Abstract

This study deals with breast cancer therapy with fractional derivative in porous medium. The classical model of energy balance equation can be generalized to some fractional derivatives namely, Caputo (C) with singular kernel and Atangana-Baleanu (ABC) with non-singular kernel. We have found the semi exact solutions of initial value problem via Laplace transform. Hyperthermia technique named as a moderate method for the treatment of breast cancer. Graphical illustration is provided for numerical values of embedded parameters with the help of MATHCAD software. As a result, a steady-state time required the therapeutic temperature point to get the death of tumor cell has been computed. A comparison has also been drawn between the solutions of fractional models with fractional derivatives and found that Atangana-Baleanu fractional model is well suited in exhibiting the memory effect of the temperature function. The findings of this research may serve the advantage that it is affordable and important in clinical or medical practice.