Abstract
We consider the well-posedness of the initial-boundary value problem for a time-fractional partial differential equation with the fractional order lying in (1,2]. For the case of time-dependent coefficients, it is difficult to give an explicit solution formula by the eigenfunction expansion method. In order to deal with the case of time-varying coefficients, we first show the unique existence and regularity of solution to a system of time-fractional ordinary differential equations. Then, the unique differential equation and improved regularity are derived by using the Galerkin method.
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Kapsamı
Uluslararası
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Type
Hakemli
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Index info
WOS.SCI
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Language
English
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Article Type
None
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Keywords
Time-fractional diffusion/wave equation Initial-boundary value problem Fredholm alternative Galerkin approximation Regularity estimate