Abstract
Fractal-fractional derivatives, which are still rather new, are frequently used to look into the complexities of an issue. Today, tumors are a prevalent and difficult-to-treat condition. The Caputo-Fabrizio-fractal-fractional derivative, which is a non-singular derivative,. has been used to explore the tumor-growth model quantitatively and numerically. By using fixed-point theorems, it has been demonstrated that the model underneath the Caputo-Fabrizio-fractal-fractional derivative exists and is unique. The Ulam-Hyres stability of the model was evaluated using non-linear analysis. Using Lagrangian-piecewise interpolation and the fundamentals of fractional calculus, we can develop an algorithm that will enable us to determine the numerical solutions for the new model. In order to show the method’s dependability and effectiveness, numerical simulations are also included. Utilizing an exponential-decay kernel, we evaluated the dynamics of the Tumor Growth model to see if the non-singular fractal fractional operator offered better dynamics for the model under consideration.