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

Nasser Sweilam¹, Seham Al-Mekhlafi^2,*, Aya Ahmed³, Ahoud Alsheri⁴, Emad Abo-Eldahab³
1 Mathematics Department, Faculty of Science, Cairo University, Giza, 12613, Egypt
2 Mathematics Department, Faculty of Education, Sana’a University, Sana’a, 1247, Yemen
3 Mathematics Department, Faculty of Science, Helwan University, Cairo, 11795, Egypt
4 Department of Mathematics, College of Science, University of Bisha, Al Namas, 67398-5644, Saudi Arabia
* Corresponding Author: Seham Al-Mekhlafi. Email: email
(This article belongs to the Special Issue: Computer Modelling for Safer Built Environment and Smart Cities)

Computer Modeling in Engineering & Sciences https://doi.org/10.32604/cmes.2024.047896

Received 21 November 2023; Accepted 26 February 2024; Published online 10 April 2024

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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.

Keywords

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

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

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