Stochastic evolution equation with Riesz-fractional derivative and white noise on the half-line

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• 作者：Martin P. Arciga Alejandre ; ^{mparciga@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Francisco J. Ariza Hernandez ; ^{aarizahfj@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Jorge Sanchez Ortiz ; ^{jsanchezmate@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Fokas method ; Fractional derivative ; Brownian motion
• 刊名：Applied Numerical Mathematics
• 出版年：2016
• 出版时间：June 2016
• 年：2016
• 卷：104
• 期：Complete
• 页码：103-109
• 全文大小：381 K

文摘

In this work, we consider an initial boundary-value problem for a stochastic evolution equation with Riesz-fractional spatial derivative and white noise on the half-line, where hmlsrc">he MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0168927415000884&_mathId=si2.gif&_user=111111111&_pii=S0168927415000884&_rdoc=1&_issn=01689274&md5=1f71abf8166ebe727e87f6d775785ee2">height="15" width="21" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0168927415000884-si2.gif">hContainer hidden">hCode">h altimg="si2.gif" overflow="scroll">hvariant="script">Dxαh> is the Riesz-fractional derivative, hmlsrc">hImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0168927415000884&_mathId=si3.gif&_user=111111111&_pii=S0168927415000884&_rdoc=1&_issn=01689274&md5=0c338155c12eb33d663fda9bbb0ca5e0" title="Click to view the MathML source">α∈(2,3)hContainer hidden">hCode">h altimg="si3.gif" overflow="scroll">α∈hy="false">(2,3hy="false">)h>, hmlsrc">hImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0168927415000884&_mathId=si4.gif&_user=111111111&_pii=S0168927415000884&_rdoc=1&_issn=01689274&md5=2732bcaea049f81e2e68723d2eceb722" title="Click to view the MathML source">NhContainer hidden">hCode">h altimg="si4.gif" overflow="scroll">hvariant="script">Nh> is a Lipschitzian operator and hmlsrc">he MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0168927415000884&_mathId=si5.gif&_user=111111111&_pii=S0168927415000884&_rdoc=1&_issn=01689274&md5=01db2834d51cb22543cb3d2634a40c23">height="16" width="39" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0168927415000884-si5.gif">hContainer hidden">hCode">h altimg="si5.gif" overflow="scroll">B˙hy="false">(x,thy="false">)h> is the white noise. To construct the integral representation of solutions we use the Fokas method and Picard scheme to prove existence and uniqueness. Moreover, Monte Carlo methods are implemented to approximate solutions.