Stability Analysis of Fractional Differential System with Constant Delay

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Authors

  • S. Priyadharsini
     Department of Mathematics, Sri Krishna Arts and Science College, Coimbatore 641 046 ,IN

Keywords:

Stability Analysis, Fractional Order Dynamic Systems, Delay Systems.

Abstract

In this work, we analyze the stability of nonlinear fractional order delay differential equations of the form CD1/2x(t) = ax(t) + bx(t-1)x(t)+f(t, x(t)), where CD1/2 is a Caputo fractional derivative of order 1/2. Some numerical illustrations are provided to explain the proposed theory, by giving conditions on the non-linear term f(t, x(t)).

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Published

2016-12-01

How to Cite

Priyadharsini, S. (2016). Stability Analysis of Fractional Differential System with Constant Delay. The Journal of the Indian Mathematical Society, 83(3-4), 337–350. Retrieved from https://informaticsjournals.co.in/index.php/jims/article/view/6614

Issue

Volume 83, Issue 3-4, July-December 2016

Section

Articles

License

Copyright (c) 2016 S. Priyadharsini

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

 

References

R. Agarwal, J.Y. Wong and C. Li, Stability analysis of fractional differential system with Riemann-Liouville derivative, Mathematical and Computer Modelling, 52 (2010) 862-874.

Y.Chen, K.L.Moore, Analytical stability bound for a class of delayed Fractional-order dynamic systems, Nonlinear Dynamics, 29 (2002) 191-200.

W.H. Deng, C.P. Li, J.H. L, Stability analysis of linear fractional differential system with multiple time delays, Nonlinear Dynamics, 48 (2007) 409-416.

J. Gao, Y. Ding, A generalized Gronwall inequality and its application to a fractional differential equation, J. Math. Anal. Appl., 328 (2007) 1075-1081.

M.M Khader and A.S. Hendy, The approximate and exact solutions of the fractionaorder delay differential equations using Legendre Senudospectral Method, Int. J. Pure Appl. Math., 74 (2012) 287-297.

A.A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and Applications of Fractional Differential Equation, Elsevier, Amsterdam, 2006.

K.Krol, Asymptotic properties of fractional delay differential equations,Applied Mathematical Computation, 218 (2011)1515-1532.

N. MacDonald,Time lags in biological models, Springer-Verlag, Berlin, 1978.

N. MacDonald, Biological Delay Systems and Linear Stability Theory, Cambridge University Press, Cambridge, 1989.

F. Meng, X. Zhinan and Z. Huaiping, Asymptotic stability of delay differential equations via fixed point theory and applications, Canad. Appl. Math. Quart., 18 (2010) 4.

B. P. Moghaddam and Z. S. Mostaghim , A numerical method based on finite difference for solving fractiona delay differential equations, J. Taibah University for Science, 7 (2013) 120-127.

M. L. Morgado, N. J. Ford and P. M Lima, Analysis and numerical methods for fractional differential equations with delay,J. Comput. Appl. Math., 252 (2013) 159-163.

M. Moze, J. Sabatier, A. Oustaloup,LMI characterization of fractional systems stability, Advances in Fractional Calculus, 6 (2007) 419-434.

I. Podlubny, Fractional Differential Equation, Academic Press, New York, 1999.

B. Sachin, Stability analysis of class of fractional delay differential equations, Pramana, 81 (2013) 215-224.

B. Sachin and D. G. Varsha A Predictor-Corrector Scheme for solving nonlinear delay differenital equations of fractional order, J. Fractional Calculus Appl., 1 (2011) 1-9.

L. F. Shamine and S. Thompson, Numerical solution of delay differential equations, Computers and Applied Mechanical Engineering, 178 (1999) 257-262.

N. Tamas Kalma, Stability analysis of delay-differential equation method of steps and inverse Laplace transform, Differential Equations and Dynamical Systems, 17 (2009) 185-200.