Stochastic Diffusion Equation with Fractional Laplacian on the First Quadrant

被引：0
|
作者：
Jorge Sanchez-Ortiz
Francisco J. Ariza-Hernandez
Martin P. Arciga-Alejandre
Eduard A. Garcia-Murcia
机构：
[1] Universidad Autónoma de Guerrero Av. Lázaro Cárdenas S/N Cd. Universitaria Chilpancingo,Facultad de Matemáticas
来源：
Fractional Calculus and Applied Analysis | 2019年 / 22卷
关键词：
Primary 26A33; Secondary 31A10; 58J32; fractional Laplacian; Fokas method; Brownian motion; Monte Carlo integration;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this work, we consider an initial boundary-value problem for a stochastic evolution equation with fractional Laplacian and white noise on the first quadrant. To construct the integral representation of solutions we adapt the main ideas of the Fokas method and by using Picard scheme we prove its existence and uniqueness. Moreover, Monte Carlo methods are implemented to find numerical solutions for particular examples.
引用
收藏
页码：795 / 806
页数：11
相关论文
共 50 条
  • [31] High-Accuracy Time Discretization of Stochastic Fractional Diffusion Equation
    Xing Liu
    Journal of Scientific Computing, 2022, 90
  • [32] Solution of space–time fractional diffusion equation involving fractional Laplacian with a local radial basis function approximation
    J. M. Revathy
    G. Chandhini
    International Journal of Dynamics and Control, 2024, 12 : 237 - 245
  • [33] FRACTIONAL DIFFUSION EQUATION
    SCHNEIDER, WR
    WYSS, W
    HELVETICA PHYSICA ACTA, 1987, 60 (02): : 358 - 358
  • [34] PULLBACK RANDOM ATTRACTORS FOR FRACTIONAL STOCHASTIC p-LAPLACIAN EQUATION WITH DELAY AND MULTIPLICATIVE NOISE
    Zhang, Xuping
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2022, 27 (03): : 1695 - 1724
  • [35] THE FRACTIONAL DIFFUSION EQUATION
    WYSS, W
    JOURNAL OF MATHEMATICAL PHYSICS, 1986, 27 (11) : 2782 - 2785
  • [36] Unified fractional kinetic equation and a fractional diffusion equation
    Saxena, RK
    Mathai, AM
    Haubold, HJ
    ASTROPHYSICS AND SPACE SCIENCE, 2004, 290 (3-4) : 299 - 310
  • [37] Solutions of the Fractional Reaction Equation and the Fractional Diffusion Equation
    Saxena, R. K.
    Mathai, A. M.
    Haubold, H. J.
    PROCEEDINGS OF THE THIRD UN/ESA/NASA WORKSHOP ON THE INTERNATIONAL HELIOPHYSICAL YEAR 2007 AND BASIC SPACE SCIENCE: NATIONAL ASTRONOMICAL OBSERVATORY OF JAPAN, 2010, : 53 - 62
  • [38] Unified Fractional Kinetic Equation and a Fractional Diffusion Equation
    R.K. Saxena
    A.M. Mathai
    H.J. Haubold
    Astrophysics and Space Science, 2004, 290 : 299 - 310
  • [39] On a stochastic heat equation with first order fractional noises and applications to finance
    Jiang, Yiming
    Wang, Xingchun
    Wang, Yongjin
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 396 (02) : 656 - 669
  • [40] Fractional diffusion and fractional heat equation
    Angulo, JM
    Ruiz-Medina, MD
    Anh, VV
    Grecksch, W
    ADVANCES IN APPLIED PROBABILITY, 2000, 32 (04) : 1077 - 1099
12345