Investigation of Novel Modified ABC Differential Operator in Chaotic System Application with Deep Neural Networks

The main focus of the inquiry is the Newton-Leipnik system in piecewise approach. Piecewise differential and integral operator theory, as well as its applications, have grown significantly. By assessing the state of the art and approaching the subject in a methodical manner, this essay aims to provide an outcome for this circumstance. We might observe an attractor in this system. Using piecewise modelling, this system illustrates Newton-Leipnik's method. The piecewise derivatives are introduced in this study together with the Newton-Leipnik system. It is possible to approximate these piecewise derivatives using the Adams-Bashforth approach. Using detailed numerical simulations, the numerical results have been confirmed and demonstrated. Our investigation focusses on the piecewise Newton-Leipnik system with two strange attractors and its chaotic dynamics. The Newton-Leipnik system behaves in real life with piecewise patterns shown in the numerical simulations.