Finite Difference Computational Method for Trajectory Controllability of a Delayed Damped System Governed by Fractional Differential Equation
Author:
Muthukumar P.1,
Ganesh Priya B.1
Affiliation:
1. Department of Mathematics, The Gandhigram Rural Institute-Deemed University, Dindigul, Gandhigram 624302, Tamil Nadu, India e-mail:
Abstract
In this paper, the trajectory controllability (T-controllability) of a nonlinear fractional-order damped system with time delay is studied. Existence and uniqueness of solution are obtained by using the Banach fixed point theorem and Green's function. Necessary and sufficient conditions of trajectory controllable for the nonlinear system are formulated and proved under a predefined trajectory. Modified fractional finite difference method is applied to the system for numerical approximation of its solution. The applicability of this technique is demonstrated by numerical simulation of two scientific models such as neuromechanical interaction in human snoring and fractional delayed damped Mathieu equation.
Funder
Council of Scientific and Industrial Research
Science and Engineering Research Board
Publisher
ASME International
Subject
Applied Mathematics,Mechanical Engineering,Control and Systems Engineering,Applied Mathematics,Mechanical Engineering,Control and Systems Engineering