Some properties of Sadik transform and its applications of fractional-order dynamical systems in control theory

TL;DR

This paper explores new properties of the Sadik transform, including its application to fractional-order dynamical systems in control theory, supported by theoretical proofs and numerical examples.

Contribution

It introduces new properties of the Sadik transform, extends it to Caputo fractional derivatives, and applies it to fractional dynamical systems in control theory.

Findings

Established properties of Sadik transform such as integration and time delay

Proved Sadik transform theorem for Caputo fractional derivatives

Provided numerical examples validating the theoretical results

Abstract

In this paper, we study some new properties of Sadik transform such as integration, time delay, initial value theorem, and final value theorem. Moreover, we prove the theorem of Sadik transform for Caputo fractional derivative and we also establish sufficient conditions for the existence of the Sadik transform of Caputo fractional derivatives. At the end, the fractional-order dynamical systems in control theory as an application of this transform is discussed, in addition, some numerical examples to justify our results.