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

Open Access

Original research article

Author(s):

Saleh S. Redhwan^a, Sadikali L. Shaikh^b, Mohammed S. Abdo^c

^aDepartment of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad 431004 (M.S.), India
^bDepartment of Mathematics, Maulana Azad College of Arts, Science and Commerce, RozaBagh, Aurangabad 431004 (M.S.), India
^cDepartment of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad 431004 (M.S.), India

Advances in the Theory of Nonlinear Analysis and its Applications 4 (1), 51-66.

Received: November 15, 2019

Accepted: December 20, 2019

Published: December 23, 2019

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 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 are provided to justify our results.

Keywords: Fractional differential equation; Caputo fractional derivative; Integral transforms; Sadik transform.

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APA Style

Redhwan, S. S., Shaikh, S. L., & Abdo, M. S. (2019). Some properties of Sadik transform and its applications of fractional-order dynamical systems in control theory. Advances in the Theory of Nonlinear Analysis and its Application , 4 (1), 51-66.