Asymptotic stability for mixed fractional delay differential equations

Yıl 2019, Cilt: 3 Sayı: 3, 150 - 161, 31.08.2019

Abdelouaheb Ardjouni , Ahmed Hallaci Hamid Boulares

https://doi.org/10.31197/atnaa.607459

Öz

This paper is concerned with the stability analysis of nonlinear mixed fractional delay differential equations using Krasnoselskii's fixed point theorem in a weighted Banach space.

Anahtar Kelimeler

Mixed derivatives, Fractional delay differential equations, Stability, Fixed point theorems

Kaynakça

• 1) Abbas, Existence of solutions to fractional order ordinary and delay differential equations and applications, Electron. J. Differ. Equ. 2011(09) (2011), 1--11.2) R. P. Agarwal, Y. Zhou, Y. He, Existence of fractional neutral functional differential equations, Comput. Math. Appl. 59 (2010) 1095--1100. 3) B. Ahmad, S. K. Ntouyas, Existence and uniqueness of solutions for caputo-hadamard sequential fractional order neutral functional differential equations, Electronic Journal of Differential Equations, 2017(36) (2017), 1--11. 4) H. Boulares, A. Ardjouni, Y. Laskri, Stability in delay nonlinear fractional differential equations, Rend. Circ. Mat. Palermo 65 (2016) 243--253. 5) S. Das, Functional Fractional Calculus, Springer science and business media, (2011). 6) F. Ge, C. Kou, Asymptotic stability of solutions of nonlinear fractional differential equations of order 1≤α≤2, J. Shanghai Normal Univ. 44(3) (2015) 284--290. 7) F. Ge, C. Kou, Stability analysis by Krasnoselskii's fixed point theorem for nonlinear fractional differential equations. Appl. Math. Comput. 257 (2015) 308--316. 8) A. Guezane-Lakoud, R. Khaldi, A. Kilicman, Existence of solutions for a mixed fractional boundary value problem, Advances in Difference Equations, 2017(164) (2017) 1--9. 9) R. Hilfer, Application of fractional calculus in physics (pp. 699--707. World Scientific, Singapore, (2000). 10) A. Khare, Fractional statistics and quantum theory, Singapore: World Scientific, (2005). 11) A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier Science B. V., Amsterdam, (2006). 12) C. Kou, H. Zhou, Y. Yan, Existence of solutions of initial value problems for nonlinear fractional differential equations on the half-axis, Nonlinear Anal.74 (2011) 5975--5986. 13) Y. Li, Y. Chen, I. Podlunby, Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability, Comput. Math. Appl. 59 (2010) 1810--1821. 14) C. Li, F. Zhang, A survey on the stability of fractional differential equations, Eur. Phys. J. Special Topics. 193 (2011) 27--47. 15) I. Petras, Fractional-Order Nonlinear Systems Modeling Analysis and simulation, Springer science and business media, 2011. 16) I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, (1999). 17) D. R. Smart, Fixed point theorems, Cambridge university, Press, Cambridge, (1980). 18) Z. L. Wang, D. S. Yang, T. D. Ma, N. Sun, Stability analysis for nonlinear fractional-order systems based on comparison principle, Nonlinear Dyn. 75 (2014) 387--402. 19) J. Wang, Y. Zhou, M. Feckan, Nonlinear impulsive problems for fractional differential equations and Ulam stability, Comput. Math. Appl. 64 (2012) 3389--3405.