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AxiomsIn this paper, we investigate a fuzzy Hilfer fractional evolution equation of type ...
Kholoud N. Alharbi, Sanaa Alotaibi
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Fractal and Fractional, 2021 Under a new generalized definition of exact controllability we introduced and with a appropriately constructed time delay term in a special complete space to overcome the delay-induced-difficulty, we establish the sufficient conditions of the exact ...
Daliang Zhao
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Extremal Mild Solutions of Hilfer Fractional Impulsive Systems
, 2021 The well established monotone iterative technique that is used to study the existence and uniqueness of fractional impulsive system is extended to Hilfer fractional order in this paper. The results are derived by using the method of upper and lower solution and Gronwall inequality.
Raghavan, Divya, Nagarajan, Sukavanam
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Probabilistic representation for mild solution of the Navier–Stokes equations [PDF]
Mathematical Research Letters, 2021 This paper is based on a formulation of the Navier-Stokes equations developed by Iyer and Constantin \cite{Cont} , where the velocity field of a viscous incompressible fluid is written as the expected value of a stochastic process. Our contribution is to establish this probabilistic representation formula for mild solutions of the Navier-Stokes ...
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Existence of mild solutions for quasilinear integrodifferential equations with impulsive conditions
Electronic Journal of Differential Equations, 2009 We prove the existence and uniqueness of mild solutions of quasilinear integrodifferential equations with nonlocal and impulsive conditions in Banach spaces. The results are obtained by using a fixed point technique and semigroup theory. Examples are
Krishnan Balachandran +1 more
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On a second-order evolution inclusion [PDF]
Results in Nonlinear Analysis, 2018 We study a class of second-order evolution inclusions and we obtain a sufficient condition for f-local controllability along a reference trajectory.
Aurelian Cernea
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Boundary controllability of impulsive nonlinear fractional delay integro-differential system
Cogent Engineering, 2016 By using the strongly continuous semigroup theory and the Banach contraction principle, we study the boundary controllability of time varying delay impulsive nonlinear fractional integrodifferential system in Banach spaces.
Hamdy M. Ahmed
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Mild solutions for the one-dimensional Nordström–Vlasov system [PDF]
Nonlinearity, 2007 The Nordstrom-Vlasov system describes the evolution of a population of self-gravitating collisionless particles. We study the existence and uniqueness of mild solution for the Cauchy problem in one dimension. This approach does not require any derivative for the initial particle density.
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Mild solutions for a class of fractional SPDEs and their sample paths [PDF]
Journal of Evolution Equations, 2009 In this article we introduce and analyze a notion of mild solution for a class of non-autonomous parabolic stochastic partial differential equations defined on a bounded open subset $D\subset\mathbb{R}^{d}$ and driven by an infinite-dimensional fractional noise.
Sanz-Solé, Marta, Vuillermot, Pierre-A.
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ON UNIQUENESS OF MILD SOLUTIONS FOR DISSIPATIVE STOCHASTIC EVOLUTION EQUATIONS [PDF]
Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2010 In the semigroup approach to stochastic evolution equations, the fundamental issue of uniqueness of mild solutions is often "reduced" to the much easier problem of proving uniqueness for strong solutions. This reduction is usually carried out in a formal way, without really justifying why and how one can do that.
Marinelli, Carlo, Röckner, Michael
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