The Cauchy problem in a space of generalized functions for the equations possessing the fractional time derivative

DOI10.1134/S0037446611060073zbMath1235.35281MaRDI QIDQ662647

E. V. Pasichnik, A. O. Lopushanskyj, G. P. Lopushanskaya

Publication date: 24 February 2012

Published in: Siberian Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

convolutiongeneralized functionGreen functionderivative of fractional order

Mathematics Subject Classification ID

Existence problems for PDEs: global existence, local existence, non-existence (35A01) Fractional partial differential equations (35R11) Green's functions for elliptic equations (35J08) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (8)

Space-time fractional Cauchy problem in spaces of generalized functions ⋮ Fractional integral inequalities and their applications to degenerate differential equations with the Caputo fractional derivative ⋮ A problem with an integral boundary condition for a time fractional diffusion equation and an inverse problem ⋮ The Cauchy problem for the fractional diffusion equation in a weighted Hölder space ⋮ Inverse problem for $2b$-order differential equation with a time-fractional derivative ⋮ Monotone iterations method for fractional diffusion equations ⋮ Restoration of the Initial Data in the Problem for a Diffusion Equation with Fractional Derivative with Respect to Time ⋮ The Cauchy problem for an equation with fractional derivatives in Bessel potential spaces

Cites Work

• Solution of a parabolic boundary-value problem in a space of generalized functions with the help of the Green matrix
• Analytic methods in the theory of differential and pseudo-differential equations of parabolic type
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