Two different parallel approaches for a hybrid fractional order Coronavirus model

Abstract

In this paper, two different parallel approaches for a hybrid fractional order Coronavirus (2019-nCov) mathematical model are presented. Both parallel approaches are implemented using Julia high level language. Parallel algorithm implementations are developed for the HPC cluster using Message Passing Interface (MPI) technology and general-purpose computing on GPUs (GPGPU) using Compute Unified Device Architecture (CUDA) based on hardware environments. The algorithm implementation are used to solve the real-world problem of the hybrid fractional order Coronavirus (2019-nCov) mathematical model and to study the parallel efficiency. The introduced hybrid fractional order derivative is defined as a linear combination of the integral of Riemann-Liouville and the fractional order Caputo derivative. A parallel algorithm is designed based on the predictor-corrector method with the discretization of the Caputo proportional constant fractional hybrid operator for solving the model problem numerically. Simulation results show that, both the new parallel approaches achieve significant efficiency.