Numerical Solution for Fuzzy Time-Fractional Cancer Tumor Model with a Time-Dependent Net Killing Rate of Cancer Cells

SIMPLE SUMMARY: One of the most recognized phenomena is the cancer tumor which uncontrollably grows in human cells and spreads over the other parts of the body. It spreads in many forms, including bone tumors, brain tumors, organ tumors, lung and pancreatic cancer tumors and others. This led to extensive research studying the cancer tumor model to follow up on the behavior of various cancer tumors in a body. In this paper, we discuss the impact of using a fuzzy time-fractional derivative in several cases of fuzzy initial conditions for the fuzzy time-fractional cancer tumor model. It was noted that there is a substantial need to study the fuzzy fractional cancer tumor model as it provides a comprehensive understanding of the behavior of the cancer tumor by taking into account several fuzzy cases in the initial condition of the proposed model. ABSTRACT: A cancer tumor model is an important tool for studying the behavior of various cancer tumors. Recently, many fuzzy time-fractional diffusion equations have been employed to describe cancer tumor models in fuzzy conditions. In this paper, an explicit finite difference method has been developed and applied to solve a fuzzy time-fractional cancer tumor model. The impact of using the fuzzy time-fractional derivative has been examined under the double parametric form of fuzzy numbers rather than using classical time derivatives in fuzzy cancer tumor models. In addition, the stability of the proposed model has been investigated by applying the Fourier method, where the net killing rate of the cancer cells is only time-dependent, and the time-fractional derivative is Caputo’s derivative. Moreover, certain numerical experiments are discussed to examine the feasibility of the new approach and to check the related aspects. Over and above, certain needs in studying the fuzzy fractional cancer tumor model are detected to provide a better comprehensive understanding of the behavior of the tumor by utilizing several fuzzy cases on the initial conditions of the proposed model.