A modified predictor–corrector scheme with graded mesh for numerical solutions of nonlinear Ψ-caputo fractional-order systems

Abstract

The aim of this article is to develop a modified predictor–corrector scheme for solving the system of nonlinear Ψ\Psi -Caputo fractional differential equations with order 0<α<10\lt \alpha \lt 1. By using the graded mesh and considering the predictor–corrector scheme for Ψ\Psi -Caputo fractional derivative, the numerical solutions of nonlinear Ψ\Psi -Caputo fractional-order systems are derived. Moreover, the error estimations of predictor–corrector scheme with graded mesh are also investigated. Particularly, the accuracy of numerical solutions depended on the function Ψ\Psi and the partition size on graded mesh. Numerical examples for linear and nonlinear fractional differential systems with various kernels and meshes are considered to explain the value and effectiveness of the proposed schemes

Keywords

• ψ-caputo nonlinear fractional-order systems
• predictor–corrector scheme
• graded mesh
• error estimation
• 26a33
• 34a08
• 65l05