Stability, existence, and uniqueness for solving fractional glioblastoma multiforme using a Caputo–Fabrizio derivative

Abstract

In this study, fractional order is applied to the glioblastoma multiforme (GBM) and IS interaction models. The monoclonal brain tumor GBM gives rise to other tumors with varying growth rates and treatment susceptibilities once it reaches a certain density. The two populations of macrophages and activated macrophages make up the IS cells as well. Because of this, this model depicts two conversions: the transformation of a sensitive tumor cell into a resistant tumor cell and the transformation of passive macrophages into active macrophages, as well as an interaction among the tumor cell and the macrophages. The memory and nonlocalization properties of fractional derivatives make them an excellent tool for simulating the spread of epidemics. Numerous characteristics exist in the Caputo–Fabrizio fractional derivative kernel, including nonsingularity, nonlocality, and an exponential establish. For simulating disease spreading systems, it is preferred. We suggest defining the Caputo–Fabrizio fractional derivation procedure as the paradigm for the GBM disease in this work. The hypothesized fractional‐order GBM disease paradigm's stability is investigated. The hypothesized fractional‐order GBM disease paradigm's existence and originality are established. A suggested novel signal flow graph introduces the system. We have established the existence of GBM and its uniqueness. Additionally, the numerical integrations necessary for the fractional‐order glioma immune model are carried out using the predictor–corrector Adams–Bashforth–Moulton (ABM) approach for fractional‐order differential equations. These simulations demonstrate that the behavior of the model can be affected by changing the parameters for the fractional order, contact evaluation, or quarantine evaluation. The findings demonstrate how epidemiologically sound the proposed fractional model is.