Rossler’s system using piecewise derivative

This article deals with a piecewise system named piecewise Rossler’s system which exhibits a concept of piecewise derivatives based on Classical-power-law randomness, Classical Mittag-Leffler-law-randomness, and Classical fading memory randomness fractional operators. To examine the crossover and chaos patterns for Rossler’s system, we have revisited and modified Rossler’s system using the concept of a piecewise system. This paper focuses also on growing a forecasting piecewise system to establish states in chaotic aspects. The existence and uniqueness are obtained for piecewise Rossler’s system with the Caputo derivative. The numerical solutions are based on Newton interpolation. Numerical solutions have been developed to approximate these piecewise derivatives. The obtained results show real-world behaviors of Rossler’s systems with piecewise patterns at various values of order α. •Rossler’s system exhibits a concept of piecewise derivatives based on Classical power-law randomness, Classical Mittag-Leffler-law-randomness, and Classical fading memory randomness fractional operators.•This article presented a piecewise modeling to derive Rossler’s system and method for its numerical simulation.•The mathematical results are obtained and discussed.•The concept of piecewise modeling has been applied to capture the chaos and crossover behaviors of the piecewise Rossler’s system.•Rossler’s system may depict different behavior at various values of order α and parameter a.