Dynamics of Generalized Caputo Type Delay Fractional Differential Equations Using a Modified Predictor-Corrector Scheme

Abstract

In this paper, we modified the Predictor-Corrector scheme to simulate the delay differential equations in new generalised Caputo-type non-classical derivatives sense. We provided some numerical illustrations to exhibit availability of the algorithm. From the graphical simulations, we observed some periodic and chaotic natures of the given systems for different fractional order values. We believe that the presented scheme is expected to be further used to solve delay fractional differential equations in generalized Caputo type fractional-order sense. The original contribution of this research is to provide a generalised numerical algorithm to solve different fractional-order delay-type systems.