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In this paper, for the impulsive fractional integro-differential equations involving Caputo fractional derivative in Banach space, we investigate the existence and uniqueness of a pseudo almost periodic -mild solution. The working tools are based on the fixed point theorems, the fractional powers of operators and fractional calculus. Some known results are improved and generalized. Finally, existence and uniqueness of a pseudo almost periodic -mild solution of a two-dimensional impulsive fractional...
In this paper, we consider a fractional impulsive boundary value problem on infinite intervals. We obtain the existence, uniqueness and computational method of unbounded positive solutions.
We present a result on the stability of moving invariant manifolds of nonlinear uncertain impulsive differential-difference equations. The result is obtained by means of piecewise continuous Lyapunov functions and a comparison principle.
This paper is concerned with the stability of the set of trajectories of a patchy vector field, in the presence of impulsive perturbations. Patchy vector fields are discontinuous, piecewise smooth vector fields that were introduced in Ancona and Bressan (1999) to study feedback stabilization problems. For patchy vector fields in the plane, with polygonal patches in generic position, we show that the distance between a perturbed trajectory and an unperturbed one is of the same order of magnitude...
This paper is concerned with the stability of the set of trajectories
of a patchy vector field, in the presence of impulsive
perturbations.
Patchy vector fields are
discontinuous, piecewise smooth vector fields
that were introduced in Ancona and Bressan (1999)
to study feedback stabilization problems.
For patchy vector fields in the plane, with polygonal
patches in generic position, we show that the distance
between a perturbed trajectory and an unperturbed one
is of the same order of magnitude...
The work deals with non-Markov processes and the construction of systems of differential equations with delay that describe the probability vectors of such processes. The generating stochastic operator and properties of stochastic operators are used to construct systems that define non-Markov processes.
In this paper, we study a kind of fractional differential system with impulsive effect and find the formula of general solution for the impulsive fractional-order system by analysis of the limit case (as impulse tends to zero). The obtained result shows that the deviation caused by impulses for fractional-order system is undetermined. An example is also provided to illustrate the result.
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