The Collocation Method Based on the New Chebyshev Cardinal Functions for Solving Fractional Delay Differential Equations

Abstract

The Chebyshev cardinal functions based on the Lobatto grid are introduced and used for the first time to solve the fractional delay differential equations. The presented algorithm is based on the collocation method, which is applied to solve the corresponding Volterra integral equation of the given equation. In the employed method, the derivative and fractional integral operators are expressed in the Chebyshev cardinal functions, which reduce the computational load. The method is characterized by its simplicity, adherence to boundary conditions, and high accuracy. An exact analysis has been provided to demonstrate the convergence of the scheme, and illustrative examples validate our investigation.

Keywords

• Chebyshev cardinal functions
• Lobatto grid
• delay differential equations
• collocation method