Fractional order Bell wavelet method for Gompertz Liver-Tumor growth model

In this study, a novel and efficient collocation technique employing fractional order Bell wavelets (FOBW) is developed for obtaining the solution of the Gompertz model for Liver-Tumor growth. The Gompertz model is initially represented by a non-linear ordinary differential equation and subsequently extended to a fractional-order differential equation. Block pulse functions (BPFs) are applied in generating the operational matrices of integration (OMI) of fractional order. After transforming the system of fractional differential equations into a linear algebraic system, Newton’s method is applied to solve the resulting equations. As the first approach developed for this problem, the capabilities of our method are illustrated through numerical examples under diverse conditions. The obtained numerical results demonstrate the functionality of the FOBW-based technique and are illustrated graphically.