Stability of functional differential equations with impulses [PDF]
Journal of Mathematical Analysis and Applications, 2007 The authors establish some comparison theorems for functional differential equations (FDE) with impulses using several Lyapunov-Razumikhin. The comparison theorems are employed to develop sufficient conditions for stability theorems for FDE. An example is given to illustrate the usefulness and advantages of the results.
Kaien Liu, Xilin Fu
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Existence Results for Fractional Neutral Functional Differential Equations with Random Impulses [PDF]
Mathematics, 2015 In this paper, we investigate the existence of solutions for the fractional neutral differential equations with random impulses. The results are obtained by using Krasnoselskii’s fixed point theorem.
Annamalai Anguraj +3 more
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p-Moment stability of functional differential equations with random impulses [PDF]
Computers and Mathematics With Applications, 2006 Functional differential equations with random impulses \[ x'(t)= f(t, x_t),\;t\geq t_0,\;t\neq\xi_k,\;x(\xi_k)= I(\tau_k, x(\xi^-_k)),\;k= 1,2,\dots, x_{t_0}= \varphi\tag{1} \] are considered. The following stability conditions were obtained by using Lyapunov's method with Razumikhin condition. Theorem. Let \(x(t)\) be a solution of system (1) and \(p>
Shujin Wu
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On Impulsive Implicit ψ-Caputo Hybrid Fractional Differential Equations with Retardation and Anticipation [PDF]
Mathematics, 2022 In this paper, we investigate the existence and Ulam–Hyers–Rassias stability results for a class of boundary value problems for implicit ψ-Caputo fractional differential equations with non-instantaneous impulses involving both retarded and advanced ...
Abdelkrim Salim +3 more
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Approximate Controllability of Neutral Functional Integro-Differential Equations with State-Dependent Delay and Non-Instantaneous Impulses [PDF]
Mathematics, 2023 In this manuscript, we investigate the issue of approximate controllability for a certain class of abstract neutral integro-differential equations having non-instantaneous impulsions and being subject to state-dependent delay.
Abdelhamid Bensalem +3 more
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New Results on Impulsive Functional Differential Equations with Infinite Delays [PDF]
Abstract and Applied Analysis, 2013 We investigate the stability for a class of impulsive functional differential equations with infinite delays by using Lyapunov functions and Razumikhin-technique.
Jie Yang, Bing Xie
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Comparison results for functional differential equations with impulses
Mathematica Slovaca, 2013 Abstract Comparison principles play an important role in the qualitative and quantitative study of differential equations. In this paper, we investigate a first order functional differential equations with impulses and establish new comparison results.
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Impulsive functional‐differential equations with nonlocalconditions [PDF]
International Journal of Mathematics and Mathematical Sciences, 2002 The existence, uniqueness, and continuous dependence of a mild solution of an impulsive functional‐differential evolution nonlocal Cauchy problem in general Banach spaces are studied. Methods of fixed point theorems, of a C0 semigroup of operators and the Banach contraction theorem are applied.
Haydar Akça +2 more
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Results in Control and Optimization, 2023 For a class of impulsive fractional differential equation with fractional order r∈(1,2)by means of solution operator Sr(t), we develop the mild solution and deal with the existence results of mild solution for the considered equation with state-dependent
Ganga Ram Gautam +5 more
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Non-Instantaneous Impulsive BVPs Involving Generalized Liouville–Caputo Derivative
Mathematics, 2022 This manuscript investigates the existence, uniqueness and Ulam–Hyers stability (UH) of solution to fractional differential equations with non-instantaneous impulses on an arbitrary domain.
Ahmed Salem, Sanaa Abdullah
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