On the solutions of nonlinear stochastic fractional partial differential equations in one spatial dimension

被引：73

作者：

Debbi, L

Dozzi, M

机构：

[1] Univ Nancy 1, Inst Elie Cartan, Vandoeuvre Les Nancy, France

[2] Univ Ferhat Abbas, Fac Sci, Dept Math, El Maabouda Setif 19000, Algeria

[3] Univ Mohamed Boudiaf, Fac Sci, Dept Math, Msila 28000, Algeria

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2005年 / 115卷 / 11期

关键词：

fractional derivative operator; stochastic partial differential equation; space-time white noise; holder continuity; equation of high order;

D O I：

10.1016/j.spa.2005.06.001

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Existence, uniqueness and regularity of the trajectories of mild solutions of one-dimensional nonlinear stochastic fractional partial differential equations of order alpha > 1 containing derivatives of entire order and perturbed by space-time white noise are studied. The fractional derivative operator is defined by means of a generalized Riesz-Feller potential. (c) 2005 Elsevier B.V. All rights reserved.

引用

页码：1764 / 1781

页数：18

共 20 条

[1] Fractional diffusion and fractional heat equation [J].

Angulo, JM ;

Ruiz-Medina, MD ;

Anh, VV ;

Grecksch, W .

ADVANCES IN APPLIED PROBABILITY, 2000, 32 (04) :1077-1099

[2] Mittag-Leffler's function and stochastic linear Volterra equations of convolution type [J].

Bonaccorsi, S ;

Tubaro, L .

STOCHASTIC ANALYSIS AND APPLICATIONS, 2003, 21 (01) :61-78

[3]

Dalang R., 2003, Electronic Journal of Probability, V8, P1, DOI [10.1214/EJP.v8-123, DOI 10.1214/EJP.V8-123]

[4]

DEBBI L, IN PRESS MAGHREB MAT

[5]

DEBBI L, UNPUB SOME PROPERTIE

[6]

DEBBI L, UNPUB EXPLICIT SOLUT

[7]

Feller W., 1952, MEDDELANDEN LUNDS S, P73, DOI DOI 10.1186/S13662-017-1354-4

[8]

Gorenflo R., 1998, Fract. Calc. Appl. Anal., V1, P167

[9]

KOMATSU T, 1984, OSAKA J MATH, V21, P113

[10]

Kotelenez Peter, 1992, Stochastics Stochastics Rep., V41, P177, DOI [10.1080/17442509208833801, DOI 10.1080/17442509208833801]

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