Mittag–Leffler Stability of Impulsive Nonlinear Fractional-Order Systems with Time Delays
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Agarwal OP, Sabatier J, Machado JAT (2007) Advances in fractional calculus. Springer, Berlin
Agarwal R, Hristova S, O’Regan D (2015) Lyapunov functions and strict stability of caputo fractional differential equations. Adv Differ Equ 2015:346
Agarwal R, Hristova S, O’Regan D (2017) Mittag–Leffler stability for impulsive Caputo fractional differential equations. Differ Equ Dyn Syst 11:1–17
Area I, Nieto JJ (2021) Fractional-order logistic differential equation with Mittag–Leffler type kernel. Fractal Fract 5(4):273
Arthi G, Park JH, Suganya K (2019) Controllability of fractional order damped dynamical systems with distributed delays. Math Comput Simul 165:74–91
Arthi G, Brindha N, Ma Y-K (2021) Finite-time stability of multiterm fractional nonlinear systems with multistate time delay. Adv Differ Equ 2021:102
Baleanu D, Wu GC (2019) Some further results of the Laplace transform for variable order fractional difference equations. Fract Cal Appl Anal 22:1641–1654
Bohner M, Tunc O, Tunc C (2021) Qualitative analysis of Caputo fractional integro-differential equations with constant delays. Comput Appl Math 40:214
Dasbasi B (2021) Stability analysis of an incommensurate fractional-order SIR model. Math Model Numer Simul Appl 1:44–55
Debnath L (2003) Recent applications of fractional calculus to science and engineering. Int J Math Math Sci 54:3413–3442
Deep A, Tunc DC (2020) On the existence of solutions of some non-linear functional integral equations in Banach algebra with applications. Arab J Basic Appl Sci 27:279–286
Feckan M, Zhou Y, Wang J (2012) On the concept and existence of solution for impulsive fractional differential equations. Commun Nonlinear Sci Numer Simul 17:3050–3060
Guo TL, Jiang W (2012) Impulsive fractional functional differential equations. Comput Math Appl 64:3414–3424
Hammouch Z, Yavuz M, Ozdemir N (2021) Numerical solutions and synchronization of a variable-order fractional chaotic system. Math Model Numer Simul Appl 1:11–23
Hei X, Wu R (2016) Finite-time stability of impulsive fractional-order systems with time-delay. Appl Math Model 40:4285–4290
Khan H, Tunc C, Khan A (2020) Stability results and existence theorems for nonlinear delay-fractional differential equations with $$\Phi _p$$-operator. J Appl Anal Comput 10:584–597
Lakshmikantham V (2008) Theory of fractional functional differential equations. Nonlinear Anal Theory Methods Appl 69:3337–3343
Lazarevic MP, Spasic AM (2009) Finite-time stability analysis of fractional order time-delay systems: Gronwall’s approach. Math Comput Model 49:475–481
Li M, Wang J (2018) Exploring delayed Mittag–Leffler type matrix functions to study finite time stability of fractional delay differential equations. Appl Math Comput 324:254–265
Li Y, Chen Y, Podlubny I, Cao Y (2009) Mittag–Leffler stability of fractional order nonlinear dynamic systems. Automatica 45:1965–1969
Li Y, Chen Y, Podulbny I (2010) Stability of fractional-order nonlinear dynamic system: Lyapunov direct method and generalized Mittag–Leffler stability. Comput Math Appl 15:1810–1821
Li X, Liu S, Jiang W, Zhou X (2012) Mittag–Leffler stability of nonlinear fractional neutral singular systems. Commun Nonlinear Sci Numer Stimul 17:3961–3966
Li H et al (2015) Global Mittag–Leffler stability of coupled system of fractional-order differential equations on network. Appl Math Comput 270:269–277
Li X, Liu S, Jiang W (2018) q-Mittag–Leffler stability and Lyapunov direct method for differential systems with q-fractional order. Adv Differ Equ 2018:78
Martnez-Fuentes O, Martnez-Guerra R (2018) A novel Mittag–Leffler stable estimator for nonlinear fractional-order systems: a linear quadratic regulator approach. Nonlinear Dyn 94:1973–1986
Miller KS, Ross B (1993) An introduction to fractional calculus and fractional differential equations. Wiley, New York
Naik PA, Yavuz M, Qureshi S, Zu J, Townley S (2020) Modeling and analysis of COVID-19 epidemics with treatment in fractional derivatives using real data from Pakistan. Eur Phys J Plus 135:1–42
Ren F, Cao F, Cao J (2015) Mittag–Leffler stability and generalized Mittag–Leffler stability of fractional-order gene regulatory networks. Neurocomputing 160:185–190
Sene N (2019) On the stability analysis of the fractional nonlinear systems with Hurwitz state matrix. J Fract Cal Appl 10:1–9
Sene N (2020) Mittag–Leffler input stability of fractional differential equations and its applications. Am Inst Math Sci 13:867–880
Slynko V, Tunc C (2019) Stability of abstract linear switched impulsive differential equations. Automatica 107:433–441
Stamova IM, Stamov GT (2016) Functional and impulsive differential equations of fractional-order. A Science Publisher’s Books, Qualitative analysis and applications
Stamova IM (2015) Mittag–Leffler stability of impulsive differential equations of fractional order. Q Appl Math 73:525–535
Tabouche N et al (2021) Existence and stability analysis of solution for Mathieu fractional differential equations with applications on some physical phenomena. Iran J Sci Technol Trans A Sci 45:973–982
Wu G, Baleanu D, Zeng S (2018a) Finite-time stability of discrete fractional delay systems: Gronwall inequality and stability criterion. Commun Nonlinear Sci Numer Simul 57:299–308
Wu G, Baleanu D, Huang L (2018b) Novel Mittag–Leffler stability of linear fractional delay difference equations with impulse. Appl Math Lett 82:71–78
Yang X, Li C, Huang T, Song Q (2017) Mittag–Leffler stability analysis of nonlinear fractional-order systems with impulses. Appl Math Comput 293:416–422
Yavuz M (2022) European option pricing models described by fractional operators with classical and generalized Mittag–Leffler kernels. Numer Methods Partial Differ Equ 38:434–456
Yavuz M, Abdeljawad T (2020) Nonlinear regularized long-wave models with a new integral transformation applied to the fractional derivative with power and Mittag–Leffler kernel. Adv Differ Equ 2020:1–18
Yavuz M, Sene N (2020) Stability analysis and numerical computation of the fractional predator-prey model with the harvesting rate. Fract Fraction 4:35
Yavuz M, Ozdemir N, Baskonus HM (2018) Solutions of partial differential equations using the fractional operator involving Mittag–Leffler kernel. Eur Phys J Plus 133:1–11
Yavuz M, Sulaiman TA, Yusuf A, Abdeljawad T (2021) The Schrodinger–KdV equation of fractional order with Mittag–Leffler nonsingular kernel. Alex Eng J 60:2715–2724