ABSTRACT
The present work addresses a fractional-order mathematical model handling an auto-immune condition against the thyroid follicle cells, Hashimoto’s thyroiditis (HT). Under this condition, the thyroid-stimulating hormone (TSH) changes more rapidly than the free thyroxine (FT4), resulting in the thyroid follicle cells getting destroyed by the interrupted working process of the hypothalamus-pituitary-thyroid (HPT) axis. We address the modernization of an existing 4d-model of HT by incorporating the fractional-order operators . The proposed fractional-order model comprises four time-dependent variables namely, TSH, FT4, anti-thyroid antibodies (Ab), and size of the thyroid gland (T). We discuss the local stability conditions for the recommended problem of fractional-order, followed by constructing a numerical solution scheme. We implement the Adomian decomposition method (ADM) on the extended fractional model of HT to retrieve the approximate solutions. In addition, we plot the time-dependent state variables involved to interpret the numerical results effectively.
