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Non-Instantaneous Impulses in Caputo Fractional Differential Equations [PDF]

Fractional Calculus and Applied Analysis, 2017
Recent modeling of real world phenomena give rise to Caputo type fractional order differential equations with non-instantaneous impulses. The main goal of the survey is to highlight some basic points in introducing non-instantaneous impulses in Caputo ...
Ravi P Agarwal, Snezhana Hristova, Donal O’Regan   +2 more
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Stability of impulsive stochastic functional differential equations with delays

Applied Mathematics Letters
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jingxian Guo, Shuihong Xiao, Jianli Li
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Stability of sets of functional differential equations with impulse effect

Applied Mathematics and Computation, 2011
The stability of sets is more general than the known stability which concerns the trivial solution, or a nontrivial solution. The stability of sets is a special stability, in terms of two measures. In this paper the author discusses the stability of sets for functional differential equations with impulses.
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Approximation of solutions to impulsive functional differential equations

Journal of Applied Mathematics and Computing, 2009
The authors consider the impulsive semilinear functional differential equation \[ u'(t)+ Au(t)=f(t,u_t),\quad t\in (0,T), \;t\neq t_k, \] \[ \Delta u(t_k)=I_k(u(t_k)), \quad k=1,2,\dots, p,\tag{1} \] \[ u(t)=h(t), \quad t\in [-\tau,0], \] where \(-A\) is the infinitesimal generator of an analytic semigroup on a separable Hilbert space \(H\), \(I_k:H\to
Muslim, M., Agarwal, Ravi P.
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Impulsive Functional-Differential Equations of Fractional Order with Variable Moments

Ukrainian Mathematical Journal, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Impulsive Semi-linear Functional Differential Equations

2015
In this chapter, we shall prove the existence of mild solutions of first order impulsive functional equations in a separable Banach space. Our approach will be based for the existence of mild solutions, on a fixed point theorem of Burton and Kirk [88] for the sum of a contraction map and a completely continuous map.
Saïd Abbas, Mouffak Benchohra
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On the solutions for impulsive fractional functional differential equations

Differential Equations and Dynamical Systems, 2009
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Chen, Fulai, Chen, Anping, Wang, Xiaoping   +2 more
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Impulsive semilinear functional differential equations

2002
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Benchohra, M., Guedda, M., Kirane, M.
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Asymptotic stability for impulsive functional differential equations

Applied Mathematics and Mechanics, 2009
To a nonlinear scalar impulsive functional differential equation the second Lyapunov method and Jensen's inequality are applied to obtain new asymptotic stability results. An interesting example of an equation with infinite number of terms is considered.
Luo, Zhi-guo, Luo, Yan
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Impulsive Partial Hyperbolic Functional Differential Equations

2012
In this chapter, we shall present existence results for some classes of initial value problems for fractional order partial hyperbolic differential equations with impulses at fixed or variable times impulses.
Saïd Abbas, Mouffak Benchohra, Gaston M. N’Guérékata   +2 more
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