TY  - EJOU
AU  - Sweilam, Nasser 
AU  - Al-Mekhlafi, Seham 
AU  - Ahmed, Aya 
AU  - Alsheri, Ahoud 
AU  - Abo-Eldahab, Emad 

TI  - Numerical Treatments for Crossover Cancer Model of Hybrid Variable-Order Fractional Derivatives
T2  - Computer Modeling in Engineering \& Sciences

PY  - 2024
VL  - 140
IS  - 2
SN  - 1526-1506

AB  - 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.
KW  - Cancer diseases; hybrid variable-order fractional derivatives; adams bashfourth fifth step; generalized fifth order Runge-Kutta method

DO  - 10.32604/cmes.2024.047896