共查询到20条相似文献,搜索用时 15 毫秒
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We will prove the existence, uniqueness and regularity of the solution for a stochastic fractional partial differential equation driven by an additive fractional space–time white noise. Moreover, the absolute continuity of the solution is also obtained. 相似文献
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We study a class of stochastic fractional partial differential equations of order α>1 driven by a (pure jump) Lévy space–time white noise and a fractional noise. We prove the existence and uniqueness of the global mild solution by the fixed point principle under some suitable assumptions. 相似文献
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We study the existence,uniqueness and Hlder regularity of the solution to a stochastic semilinear equation arising from 1-dimensional integro-differential scalar conservation laws.The equation is driven by double-parameter fractional noises.In addition,the existence and moment estimate are also obtained for the density of the law of such a solution. 相似文献
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A. V. Pskhu 《Differential Equations》2014,50(1):135-139
We study the continuation of solutions of a fractional partial differential equation. We show that a solution can be uniquely continued into a domain that is uniquely determined by the boundary part supporting the initial conditions and outside which the continuation is no longer unique. 相似文献
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In this paper, a fractional partial differential equation subject to the Robin boundary condition is considered. Based on the properties of Riemann-Liouville fractional derivative and a generalized Riccati technique, we obtained sufficient conditions for oscillation of the solutions of such equation. Examples are given to illustrate the main results. 相似文献
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A. V. Pskhu 《Differential Equations》2011,47(3):382-392
We construct a fundamental solution of a linear fractional partial differential equation. For an equation with Dzhrbashyan-Nersesyan
fractional differentiation operators, we solve a boundary value problem and find a closed-form representation for its solution.
The corresponding results for equations with Riemann-Liouville and Caputo derivatives are special cases of the assertions
proved here. 相似文献
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L. Kh. Gadzova 《Differential Equations》2014,50(1):122-127
For a linear ordinary differential equation with constant coefficients, we construct a solution of a boundary value problem. We prove the existence of a regular solution of this problem and derive a condition for its uniqueness. 相似文献
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Ciplea Sorina Anamaria Lungu Nicolaie Marian Daniela Rassias Themistocles M. 《Aequationes Mathematicae》2023,97(4):649-657
Aequationes mathematicae - In this paper we will study Hyers-Ulam stability for a general linear partial differential equation of first order in a Banach space. 相似文献
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Teodor M. Atanackovi? Ljubica Oparnica 《Journal of Mathematical Analysis and Applications》2007,328(1):590-608
We study the existence and the uniqueness of mild and classical solutions for a class of equations of the form . Such equations arise in distributed derivatives models of viscoelasticity and system identification theory. We also formulate a variational principle for a more general equation based on a method of doubling of variables for such equations. 相似文献
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Kijung Lee 《Journal of Mathematical Analysis and Applications》2009,353(1):24-42
We develop an Lp theory for the Cauchy problem of linear partial differential systems of the form
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An implicit unconditional stable difference scheme is presented for a kind of linear space–time fractional convection–diffusion equation. The equation is obtained from the classical integer order convection–diffusion equations with fractional order derivatives for both space and time. First-order consistency, unconditional stability, and first-order convergence of the method are proven using a novel shifted version of the classical Grünwald finite difference approximation for the fractional derivatives. A numerical example with known exact solution is also presented, and the behavior of the error is examined to verify the order of convergence. 相似文献
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We study the existence and uniqueness of the global mild solution for a stochastic fractional partial differential equation driven by a Lévy space-time white noise. Moreover, the flow property for the solution is also studied. 相似文献
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Richard E. Ewing 《Journal of Mathematical Analysis and Applications》1979,71(1):167-186
Numerical approximation of the solution of the Cauchy problem for the linear parabolic partial differential equation is considered. The problem: (p(x)ux)x ? q(x)u = p(x)ut, 0 < x < 1,0 < t? T; ; ; p(0) ux(0, t) = g(t), 0 < t0 ? t ? T, is ill-posed in the sense of Hadamard. Complex variable and Dirichlet series techniques are used to establish Hölder continuous dependence of the solution upon the data under the additional assumption of a known uniform bound for ¦ u(x, t)¦ when 0 ? x ? 1 and 0 ? t ? T. Numerical results are obtained for the problem where the data ?1, ?2 and g are known only approximately. 相似文献
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A. V. Pskhu 《Differential Equations》2016,52(12):1610-1623
We solve a boundary value problem for a first-order partial differential equation in a rectangular domain with a fractional discretely distributed differentiation operator. The fractional differentiation is given by Dzhrbashyan–Nersesyan operators. We construct a representation of the solution and prove existence and uniqueness theorems. The results remain valid for the corresponding equations with Riemann–Liouville and Caputo derivatives. In terms of parameters defining the fractional differential operator, we derive necessary and sufficient conditions for the solvability of the problem. 相似文献