New concept in calculus: Piecewise differential and integral operators

In the last decades, many methodologies have been suggested to depict behaviors of some complex world's problems arising in many academic fields. One of these problems is the multi-steps behavior displayed by some problems. A concept of piecewise derivative is introduced in this paper with the aim to model real world problems following multiples processes. We have presented some important properties of these definitions. We considered different scenarios and presented numerical schemes that could be used to solve such problems. Illustrative examples, including chaotic and epidemiological models are presented to see the effectiveness of the suggested concept. (c) 2021 Elsevier Ltd. All rights reserved.

Automated summary

This paper introduces the concept of piecewise derivative to model the multi-steps behavior of complex world problems, discussing its important properties, proposing numerical schemes for problem-solving, and validating the effectiveness of the suggested concept through illustrative examples.