Research Article

Asymptotic stability for mixed fractional delay differential equations

Volume: 3 Number: 3 August 31, 2019
EN

Asymptotic stability for mixed fractional delay differential equations

Abstract

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.

Keywords

References

  1. 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.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Publication Date

August 31, 2019

Submission Date

August 20, 2019

Acceptance Date

September 26, 2019

Published in Issue

Year 2019 Volume: 3 Number: 3

APA
Ardjouni, A., Hallaci, A., & Boulares, H. (2019). Asymptotic stability for mixed fractional delay differential equations. Advances in the Theory of Nonlinear Analysis and Its Application, 3(3), 150-161. https://doi.org/10.31197/atnaa.607459
AMA
1.Ardjouni A, Hallaci A, Boulares H. Asymptotic stability for mixed fractional delay differential equations. ATNAA. 2019;3(3):150-161. doi:10.31197/atnaa.607459
Chicago
Ardjouni, Abdelouaheb, Ahmed Hallaci, and Hamid Boulares. 2019. “Asymptotic Stability for Mixed Fractional Delay Differential Equations”. Advances in the Theory of Nonlinear Analysis and Its Application 3 (3): 150-61. https://doi.org/10.31197/atnaa.607459.
EndNote
Ardjouni A, Hallaci A, Boulares H (August 1, 2019) Asymptotic stability for mixed fractional delay differential equations. Advances in the Theory of Nonlinear Analysis and its Application 3 3 150–161.
IEEE
[1]A. Ardjouni, A. Hallaci, and H. Boulares, “Asymptotic stability for mixed fractional delay differential equations”, ATNAA, vol. 3, no. 3, pp. 150–161, Aug. 2019, doi: 10.31197/atnaa.607459.
ISNAD
Ardjouni, Abdelouaheb - Hallaci, Ahmed - Boulares, Hamid. “Asymptotic Stability for Mixed Fractional Delay Differential Equations”. Advances in the Theory of Nonlinear Analysis and its Application 3/3 (August 1, 2019): 150-161. https://doi.org/10.31197/atnaa.607459.
JAMA
1.Ardjouni A, Hallaci A, Boulares H. Asymptotic stability for mixed fractional delay differential equations. ATNAA. 2019;3:150–161.
MLA
Ardjouni, Abdelouaheb, et al. “Asymptotic Stability for Mixed Fractional Delay Differential Equations”. Advances in the Theory of Nonlinear Analysis and Its Application, vol. 3, no. 3, Aug. 2019, pp. 150-61, doi:10.31197/atnaa.607459.
Vancouver
1.Abdelouaheb Ardjouni, Ahmed Hallaci, Hamid Boulares. Asymptotic stability for mixed fractional delay differential equations. ATNAA. 2019 Aug. 1;3(3):150-61. doi:10.31197/atnaa.607459