The Cauchy problem in a space of generalized functions for the equations possessing the fractional time derivative
type: Item
instance of: scholarly article
title: The Cauchy problem in a space of generalized functions for the equations possessing the fractional time derivative
zbMATH Open document ID: 1235.35281
DOI: 10.1134/S0037446611060073
author: Andrij Lopushans'kyj
author: E. V. Pasichnik
author: Galyna Lopushans'ka
published in: Siberian Mathematical Journal
publication date: 2012-02-24T00:00:00Z
review text: The Green's vector-function is introduced to solve the Cauchy problem for equations with right-hand side and initial condition possessing a fractional time derivative and generalized functions. By studying the properties of the adjoint Green's operators, the authors prove the existence and uniqueness of the solutions to the Cauchy problem.
Mathematics Subject Classification ID: 35R11
Mathematics Subject Classification ID: 35J08
Mathematics Subject Classification ID: 35A01
Mathematics Subject Classification ID: 35A02
zbMATH DE Number: 6009098
zbMATH Keywords: generalized function
zbMATH Keywords: convolution
zbMATH Keywords: derivative of fractional order
zbMATH Keywords: Green function
reviewed by: Zhenhai Liu
MaRDI profile type: Publication
cites work: Q4001685
cites work: Q3497485
cites work: Analytic methods in the theory of differential and pseudo-differential equations of parabolic type
cites work: Solution of a parabolic boundary-value problem in a space of generalized functions with the help of the Green matrix
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cites work: Q5467952
description: scientific article; zbMATH DE number 6009098