Numerical Treatments for Crossover Cancer Model of Hybrid Variable-Order Fractional Derivatives

Abstract

In this paper, two crossover hybrid variable-order derivatives of the cancer model are developed. Grünwald-Letnikov approximation is used to approximate the hybrid fractional and variable-order fractional operators. The existence, uniqueness, and stability of the proposed model are discussed. Adams Bashfourth’s fifth-step method with a hybrid variable-order fractional operator is developed to study the proposed models. Comparative studies with generalized fifth-order Runge-Kutta method are given. Numerical examples and comparative studies to verify the applicability of the used methods and to demonstrate the simplicity of these approximations are presented. We have showcased the efficiency of the proposed method and garnered robust empirical support for our theoretical findings.