Results 1 to 10 of about 1,036,048 (312)
Mild Solutions of Quantum Stochastic Differential Equations [PDF]
Electronic Communications in Probability, 2000 We introduce the concept of a mild solution for the right Hudson-Parthasarathy quantum stochastic differential equation, prove existence and uniqueness results, and show the correspondence between our definition and similar ideas in the theory of classical stochastic differential equations.
Franco Fagnola, Stephen J. Wills
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Mild Solutions for Fractional Differential Equations with Nonlocal Conditions [PDF]
Advances in Difference Equations, 2010 This paper is concerned with the existence and uniqueness of mild solution of the fractional differential equations with nonlocal conditions , in a Banach space , where . General existence and uniqueness theorem, which extends many previous results, are given.
Fang Li
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Remark on uniqueness of mild solutions to the Navier–Stokes equations
Journal of Functional Analysis, 2004 AbstractWe investigate a limiting uniqueness criterion to the Navier–Stokes equations. We prove that the mild solution is unique under the class C([0,T);bmo-1)∩Lloc∞((0,T);L∞), where bmo-1 is the “critical” space including Ln. As an application of uniqueness theorem, we also consider the local well-posedness of Navier–Stokes equations in bmo-1.
Hideyuki Miura
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Qualitative analysis of nonlinear implicit neutral differential equation of fractional order
AIMS Mathematics, 2021 In this paper, we discuss sufficient conditions for the existence of solutions for a class of Initial value problem for an neutral differential equation involving Caputo fractional derivatives. Also, we discuss some types of Ulam stability for this class
H. H. G. Hashem, Hessah O. Alrashidi
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AIMS Mathematics, 2022 This article contracts through Cauchy problems in infinite-dimensional Banach spaces towards a system of nonlinear non-autonomous mixed type integro-differential fractional evolution equation by nonlocal conditions through noncompactness measure (MNC ...
Naveed Iqbal +4 more
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Известия Иркутского государственного университета: Серия "Математика", 2022 In this work, we will introduce a fractional Duhamel principle and use it to establish the well-boundedness and stability of a mild solution to an original fractional stochastic equation with initial data.
N. Bouteraa
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Asymptotic properties of the parabolic equation driven by stochastic measure
Modern Stochastics: Theory and Applications, 2022 A stochastic parabolic equation on $[0,T]\times \mathbb{R}$ driven by a general stochastic measure, for which we assume only σ-additivity in probability, is considered. The asymptotic behavior of its solution as $t\to \infty $ is studied.
Boris Manikin
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Fractional evolution equation nonlocal problems with noncompact semigroups [PDF]
Opuscula Mathematica, 2016 This paper is concerned with the existence results of mild solutions to the nonlocal problem of fractional semilinear integro-differential evolution equations.
Xuping Zhang, Pengyu Chen
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Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2022 In this manuscript the existence of the fractional-order functional differential inclusions [FFDI] with state-dependent delay [SDD] is investigated within the Mittag-Leffler kernel.
Arjunan Mani Mallika +2 more
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Irregular convergence of mild solutions of semilinear equations [PDF]
Journal of Mathematical Analysis and Applications, 2019 We prove that even irregular convergence of semigroups of operators implies similar convergence of mild solutions of the related semi-linear equations with Lipschitz continuous nonlinearity. This result is then applied to three models originating from mathematical biology: shadow systems, diffusions on thin layers, and dynamics of ...
Adam Bobrowski, Markus Kunze
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