Parallel computations for fractional variable-order monkeypox disease mathematical model using a hybrid GPU‒CPU framework

This paper presents an innovative parallel computational methodology employing adaptive fractional differential operators to address Monkeypox epidemiological modeling challenges. The complex dynamics of such models often present computational challenges. To address these, we develop a productive hybrid graphics processing unit–central processing unit (GPU–CPU) parallel approach. Using fractional differentiation operators, the presented approach focuses on managing the memory component of disease transmission dynamics. Our parallel method significantly reduces the calculation time and improves the overall performance of solving the Monkeypox disease model by utilizing the computing capabilities of both GPU and CPU cores. In this paper, we provide a hybrid variable-order fractional derivative that combines the variable-order fractional Caputo derivative with the integral of Riemann-Liouville. A predictor-corrector method with discretization of the Caputo proportional constant variable-order fractional hybrid operator is applied for numerical solutions. Julia, a high-level programming language, was chosen to implement the hybrid parallel technique. According to the results of the simulation, parallel approaches significantly increase productivity and efficiency.