An Accurate Approach to Simulate the Fractional Delay Differential Equations

Abstract

The fractional Legendre polynomials (FLPs) that we present as an effective method for solving fractional delay differential equations (FDDEs) are used in this work. The Liouville–Caputo sense is used to characterize fractional derivatives. This method uses the spectral collocation technique based on FLPs. The proposed method converts FDDEs into a set of algebraic equations. We lay out a study of the convergence analysis and figure out the upper bound on error for the approximate solution. Examples are provided to demonstrate the precision of the suggested approach.

Keywords

• FDDEs
• orthogonal system
• spectral collocation technique
• convergence analysis
• fractional-order Legendre polynomials