{"@context":{"@vocab":"https://cir.nii.ac.jp/schema/1.0/","rdfs":"http://www.w3.org/2000/01/rdf-schema#","dc":"http://purl.org/dc/elements/1.1/","dcterms":"http://purl.org/dc/terms/","foaf":"http://xmlns.com/foaf/0.1/","prism":"http://prismstandard.org/namespaces/basic/2.0/","cinii":"http://ci.nii.ac.jp/ns/1.0/","datacite":"https://schema.datacite.org/meta/kernel-4/","ndl":"http://ndl.go.jp/dcndl/terms/","jpcoar":"https://github.com/JPCOAR/schema/blob/master/2.0/"},"@id":"https://cir.nii.ac.jp/crid/1363670320070201856.json","@type":"Article","productIdentifier":[{"identifier":{"@type":"DOI","@value":"10.1063/1.528578"}},{"identifier":{"@type":"URI","@value":"https://pubs.aip.org/aip/jmp/article-pdf/30/1/134/19018041/134_1_online.pdf"}}],"dc:title":[{"@value":"Fractional diffusion and wave equations"}],"description":[{"type":"abstract","notation":[{"@value":"<jats:p>Diffusion and wave equations together with appropriate initial condition(s) are rewritten as integrodifferential equations with time derivatives replaced by convolution with tα−1/Γ(α), α=1,2, respectively. Fractional diffusion and wave equations are obtained by letting α vary in (0,1) and (1,2), respectively. The corresponding Green’s functions are obtained in closed form for arbitrary space dimensions in terms of Fox functions and their properties are exhibited. In particular, it is shown that the Green’s function of fractional diffusion is a probability density.</jats:p>"}]}],"creator":[{"@id":"https://cir.nii.ac.jp/crid/1380857594499808267","@type":"Researcher","foaf:name":[{"@value":"W. R. Schneider"}],"jpcoar:affiliationName":[{"@value":"Asea Brown Boveri Corporate Research, CH-5405 Baden, Switzerland"}]},{"@id":"https://cir.nii.ac.jp/crid/1383670320070201857","@type":"Researcher","foaf:name":[{"@value":"W. Wyss"}],"jpcoar:affiliationName":[{"@value":"Department of Physics, University of Colorado, Boulder, Colorado 80309"}]}],"publication":{"publicationIdentifier":[{"@type":"PISSN","@value":"00222488"},{"@type":"EISSN","@value":"10897658"}],"prism:publicationName":[{"@value":"Journal of Mathematical Physics"}],"dc:publisher":[{"@value":"AIP Publishing"}],"prism:publicationDate":"1989-01-01","prism:volume":"30","prism:number":"1","prism:startingPage":"134","prism:endingPage":"144"},"reviewed":"false","url":[{"@id":"https://pubs.aip.org/aip/jmp/article-pdf/30/1/134/19018041/134_1_online.pdf"}],"createdAt":"2002-07-26","modifiedAt":"2024-02-10","relatedProduct":[{"@id":"https://cir.nii.ac.jp/crid/1360003449882278656","@type":"Article","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Approximate Solution of Space-Time Fractional KdV Equation and Coupled KdV Equations"}]},{"@id":"https://cir.nii.ac.jp/crid/1360283694610490368","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"General time-fractional diffusion equation: some uniqueness and existence results for the initial-boundary-value problems"}]},{"@id":"https://cir.nii.ac.jp/crid/1360869855103293824","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Fractional Dissipative PDEs"}]}],"dataSourceIdentifier":[{"@type":"CROSSREF","@value":"10.1063/1.528578"},{"@type":"CROSSREF","@value":"10.7566/jpsj.89.014002_references_DOI_ReCLTqGCaMjCKvO0LHFGrTySloV"},{"@type":"CROSSREF","@value":"10.1515/fca-2016-0036_references_DOI_ReCLTqGCaMjCKvO0LHFGrTySloV"},{"@type":"CROSSREF","@value":"10.1007/978-3-031-54978-6_3_references_DOI_ReCLTqGCaMjCKvO0LHFGrTySloV"}]}