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<p>Sub–diffusive linear abstract pseudo–parabolic initial value problems with time derivatives of fractional order are studied. General conditions for the well–posedness in a complex Banach space setting are provided. The regularity of its analytic solutions is also studied with special regard to the behavior when time is near <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(0^+\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mn>0</mn> <mo>+</mo> </msup> </math></EquationSource> </InlineEquation> where fractional equations typically give rise to a lack of regularity. Numerical experiments with Artificial Neural Networks based discrete schemes making use of the regularity results as well as its outperformance are also shown.</p>

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On the regularity of linear fractional sub–diffusive pseudo–parabolic equations. The application to its discretization by means of artificial neural networks

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  • 发表日期：

    2026年5月25日

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  • Eduardo Cuesta

摘要

Sub–diffusive linear abstract pseudo–parabolic initial value problems with time derivatives of fractional order are studied. General conditions for the well–posedness in a complex Banach space setting are provided. The regularity of its analytic solutions is also studied with special regard to the behavior when time is near \(0^+\) 0 + where fractional equations typically give rise to a lack of regularity. Numerical experiments with Artificial Neural Networks based discrete schemes making use of the regularity results as well as its outperformance are also shown.