Mild Solutions
Hölder estimates of mild solutions for nonlocal SPDEs
... of mild solutions. Precisely speaking, the unique mild solution is almost surely Hölder continuous with Hölder index 0 < θ < (1/2 – d/(q α ))(1 ∧ α ...
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Local stability and parameter dependence of mild solutions for stochastic differential equations
... The rest of this paper is organized as follows. In Section , stochastic differential equa- tions with parameter are presented together with some definitions of mild solutions. In Section , existence, ...
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Existence of mild solutions for fractional evolution equations with nonlocal conditions
... The rest of this paper is organized as follows. In Section , some preliminaries are given on the fractional power of the generator of an analytic semigroup and on the mild solutions of Eq. (). In Section ...
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On mild solutions of nonlocal semilinear functional integro-differential equations
... In the present paper, we investigate the existence, uniqueness and continuous dependence on initial data of mild solutions of first order nonlocal semilinear functional integro-differential equations of ...
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Existence of mild solutions for impulsive fractional stochastic equations with infinite delay
... of solutions to stochastic differential equations (see [1, 2, 8] and references ...automorphic mild solutions to nonautonomous stochastic differential equations in Hilbert spaces by using semigroup ...
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Controllability of Mild Solutions for Evolution Equations with Infinite State-Dependent Delay
... [ 1 ] R P Agarwal, S Baghli, and M Benchohra. Controllability of mild solutions on semiinfinite interval for classes of semilinear functional and neutral functional evolution equations with infinite delay. ...
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Mild solutions to fractional differential inclusions with nonlocal conditions
... It should be pointed out that Definition can be regarded as a generalization of many previous definitions of mild solutions for various differential equations [–, –], in particular, the definitions ...
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Mild Solutions of Fractional Semilinear Integro Differential Equations on an Unbounded Interval
... method can be to apply in this work. The method we are going to use is to reduce the existence of mild solutions of fractional semilinear integro-differential equations of type (0.1) to searching a fixed ...
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On the existence of mild solutions to the Cauchy problem for a class of fractional evolution equation
... where 0 < q < 1, the fractional derivative is understood in the Caputo sense, A is an almost sectorial operator on a complex Banach space, and f, h are given functions. With the help of the theory of measure of ...
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The existence and uniqueness of mild solutions to stochastic differential equations with Lévy noise
... In this paper, we study a class of neutral stochastic differential equations (NSDEs) with the cylindrical Brownian motion and Lévy noises in an infinite-dimensional Hilbert space. The existence and uniqueness of the ...
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Existence of mild solutions for the impulsive semilinear nonlocal problem with random effects
... Zhang and Sun Advances in Difference Equations 2014, 2014 194 http //www advancesindifferenceequations com/content/2014/1/194 R ES EARCH Open Access Existence of mild solutions for the impulsive semil[.] ...
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Mild solutions of fractional evolution equations on an unbounded interval
... this subject up to now. Motivated by this, we concern ourselves with existence results for mild solutions of problem (.) in the present paper by the Tichonov fixed-point theorem. The rest of paper will be ...
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Existence and uniqueness of positive mild solutions for a class of fractional evolution equations on infinite interval
... upper solutions, we present a new result on the existence and uniqueness of positive mild solutions for the abstract fractional evolution equations by using the monotone iterative ...
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Mild Solutions for Fractional Differential Equations with Nonlocal Conditions
... Hindawi Publishing Corporation Advances in Difference Equations Volume 2010, Article ID 287861, 9 pages doi 10 1155/2010/287861 Research Article Mild Solutions for Fractional Differential Equations wi[.] ...
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Existence and uniqueness of mild solutions for a class of nonlinear fractional evolution equation
... The nonlinear fractional evolution equation is a general form for fractional ordinary dif- ferential equations, fractional partial differential equations, and fractional functional dif- ferential equations related to the ...
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Existence and dimension of the set of mild solutions to semilinear fractional differential inclusions
... of solutions to the analytic and numerical methods for finding solutions, have appeared in the literature, for instance, see [9-20] and references ...
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Existence and Uniqueness of Mild Solutions for Fractional Integrodifferential Equations
... In this paper, motivated by [1-28] (especially the estimating approaches given in [11, 12, 15, 24, 26]), we investigate the existence and uniqueness of mild solution of the equation (1.1) in a Banach space # , ...
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Existence of solutions for fractional impulsive integro-differential systems
... In the past few years, the existence, uniqueness and some other properties of mild solutions of differential and fractional evolution equations (1.1)-(1.3) with (or without impulsive) f (t, u(t), T u(t), ...
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On Nonclassical Impulsive Ordinary Differential Equations with Nonlocal Conditions
... Results on mild solutions of nonclassical differential equations with impulsive and nonlocal conditions are extended to a case when the nonlocal conditions are necessarily non Lipschitz [r] ...
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Topological properties of \(C^{0}\)-solution set for impulsive evolution inclusions
... 9. Barbu, V.: Nonlinear Semigoups and Differential Equation in Banach Space. Editura Academiei, Bucuresti (1976) 10. Benchohra, M., Abbas, S.: Advanced Functional Evolution Equations and Inclusions. Springer, Berlin ...
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