Stability Analysis of Conformable Fractional Systems

Document Type : Research Article


1 Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, P.O. Box 1914, Rasht, Iran.

2 Department of Applied Mathematics, Faculty of Mathematical Sciences, Islamic Azad University, Lahijan Branch, P.O. Box 1616, Lahijan, Iran.


‎ In this paper, we investigate stability analysis of fractional differential systems equipped with the conformable fractional derivatives. Some stability conditions of fractional differential systems are proposed by applying the fractional exponential function and the fractional Laplace transform. Moreover, we check the stability of conformable fractional Lotka-Volterra system with the multi-step homotopy perturbation method to demonstrate the efficiency and effectiveness of the proposed procedure.


1. Abdeljawad, T. On conformable fractional calculus, J. Comput. Appl. Math., 279 (2015) 57-66.
2. Abdeljawad, T., Al Horani, M., and Khalil, R. Conformable fractional semigroups of operators, J. Semigroup Theory Appl., 2015 (2015) 1-9.
3. Aminikhah, H., Refahi Sheikhani, A.H. and Rezazadeh, H. Stability analysis of distributed order fractional Chen system, The Sci. World J., 2013 (2013) 1-13.
4. Aminikhah, H., Refahi Sheikhani, A.H. and Rezazadeh, H. Stability analysis of linear distributed order system with multiple time delays, U.P.B. Scientific Bulletin-Series A-Applied Mathematics and Physics, 77 (2015) 207-218.
5. Chowdhury, M.S. and Hashim, I. Application of multistage homotopy per turbation method for the solutions of the Chen system, Nonlinear Anal. Real World Appl., 10 (2009) 381-391.
6. Deng, W., Li, C. and Lu, J. Stability analysis of linear fractional dif ferential system with multiple time delays, Nonlinear Dynam., 48 (2007) 409-416.
7. Khalil, R., Al Horani, M., Yousef, A. and Sababheh, M. A new definition of fractional derivative, J. Comput. Appl. Math., 264 (2014) 65-70.
8. Kilbas, A.A., Srivastava, H.M., Trujillo, J.J. Theory and Application of Fractional Differential Equations, Elsevier, New York, 2006.
9. Lotka, A.J. Elements of Physical Biology, Williams and Wilkins Company, Baltimore, 1925.
10. He, J.H. Homotopy perturbation technique, Comput. Methods Appl. Mech. Eng., 178 (1999) 257-262.
11. Matignon, D. Stability results for fractional differential equations with applications to control processing, Comput. Engrg. Syst. Appl., 2 (1996) 963-968.
12. Oldham, K.B., Spanier, J. The Fractional Calculus, Academic Press, New York, 2006.
13. Pielou, E. An Introduction to Mathematical Ecology, Wiley-Interscience, New York, 1969.
14. Saberi Najafi, H., Refahi Sheikhani, A.H. and Ansari, A. Stability Analysis of Distributed Order Fractional Differential Equations, Abstr. Appl. Anal., 2011 (2011) 1-12.
15. Rezazadeh, H., Aminikhah, H., and Refahi Sheikhani, A.H. Stability analysis of Hilfer fractional differential systems, Mathematical Communications, 21 (2016) 45-64.
16. Volterra, V. Fluctuations in the abundance of a species considered math ematically, Nature, 118 (1926) 558-560.
17. Vukic, Z., Kuljaca, L. Nonlinear Control Systems, CRC Press, 2003.