Stochastic fractional differential equations
Comparison principle and stability for a class of stochastic fractional differential equations
... Recently, the authors in [] studied the problem of existence and uniqueness of solu- tions of the initial value problem of stochastic fractional differential equations. But they did not discuss the ...
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Nonlocal fractional stochastic differential equations driven by fractional Brownian motion
... In this paper, we consider a class of nonlocal fractional stochastic differential equations driven by fractional Brownian motion with Hurst index H > 1 2 . Sufficient conditions for the ...
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Approximate controllability of impulsive fractional stochastic differential equations with state dependent delay
... nonlinear fractional impulsive stochastic differential system under the assumption that the corresponding linear system is approximately ...Using fractional calculus, stochastic analysis, and ...
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Error estimates of finite element methods for nonlinear fractional stochastic differential equations
... In this subsection, we first present and prove some lemmas, which are crucial for the derivation of the semidiscrete error estimate for the nonlinear fractional stochastic dif- ferential equation. Then we ...
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Modeling long range dependent Gaussian processes with application in continuous time financial models
... of fractional stochastic differential ...such fractional stochastic differential equations and the correspondence between ...the equations are discussed ...
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Existence of solutions for fractional stochastic impulsive neutral functional differential equations with infinite delay
... utilizing fractional calculations and a fixed point technique ...for fractional impulsive neutral functional differential equations with infinite delay by using the Caputo fractional derivative, ...
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Nonlocal stochastic integro differential equations driven by fractional Brownian motion
... for stochastic evolution equations with nonlocal ...of stochastic differential equations with nonlocal conditions are valid only for the Lipschitz or compact assumptions on nonlocal ...nonlocal ...
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On the non Lipschitz stochastic differential equations driven by fractional Brownian motion
... Let (, F, P) be a complete probability space. SDEs with respect to fBm have been in- terpreted via various stochastic integrals, such as the Wick integral, the Wiener integral, the Skorohod integral, and path-wise ...
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Approximate controllability of fractional impulsive neutral stochastic differential equations with nonlocal conditions
... of fractional impulsive neutral stochastic differential equations with nonlocal conditions and infinite delay in Hilbert spaces is ...and stochastic analysis theory, some sufficient conditions are ...
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Existence and uniqueness of solutions for stochastic differential equations of fractional order \(q > 1\) with finite delays
... differential equations are valuable tools for description of some systems and processes with stochastic disturbances in many fields of science and ...of stochastic differential equations, one can ...
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A white noise approach to stochastic partial differential equations driven by the fractional Lévy noise
... The remainder of this paper is organized as follows. In Sect. 2, we briefly recall the basic results on the white noise analysis for a d-parameter Lévy random field given by [5]. In Sect. 3, we define the formal derivative ...
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Stability of delayed impulsive stochastic differential equations driven by a fractional Brown motion with time varying delay
... impulsive stochastic differential equations driven by a fractional Brown motion with finite time-varying ...the fractional Brown motion belongs to ( 1 2 , 1). In terms of fractional power ...
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Attracting and quasi invariant sets of neutral stochastic integro differential equations with impulses driven by fractional Brownian motion
... In this paper, we introduced two new impulsive integral inequalities with respect to neu- tral stochastic integro-differential equations with impulses driven by fBm. We studied the attracting and ...
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Controllability of a Stochastic Neutral Functional Differential Equation Driven by a fBm
... of fractional differential equations and their applications are prominent, especially in modeling several complex phenomena such as anomalous diffusion of particles (see, for examples, [6] ...neutral ...
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Integer Versus Fractional Order SEIR Deterministic and Stochastic Models of Measles
... (Caputo) fractional differential equations depicting the susceptible-exposed-infectious-recovered (SEIR) models of ...and fractional stochastic processes, we introduce the ...
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A class of Hilfer fractional stochastic differential equations and optimal controls
... Hilfer fractional stochastic differential equations with nonlocal ...these equations by means of stochastic analysis theory, fractional calculations, and operator semigroup ...
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Exponential stability of fractional stochastic differential equations with distributed delay
... by fractional Brownian motion are attracting more and more ...considers fractional stochastic differential equations with distributed ...
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Regularity of the Solutions to SPDEs in Metric Measure Spaces
... of stochastic equations considered in the paper by Hinz and Z¨ahle [24, Section ...consider stochastic partial differential equations driven by fractional Brownian noises on ...
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On existence results for impulsive fractional neutral stochastic integro differential equations with nonlocal and state dependent delay conditions
... On the one hand, various evolutionary processes from fields in physics, population dy- namics, aeronautics, economics, and engineering are characterized by the fact that they undergo abrupt changes of state at certain ...
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Boundary controllability of nonlocal Hilfer fractional stochastic differential systems with fractional Brownian motion and Poisson jumps
... ential equations of order 1 < q < 2 with infinite delay and Poisson ...the fractional stochastic differential equations with Hilfer fractional derivative, with Poisson jumps and ...
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