Notes on Convergence Results for Parabolic Equations with Riemann–Liouville Derivatives

Notes on Convergence Results for Parabolic Equations with Riemann–Liouville Derivatives

Fractional diffusion equations have applications in various fields and in this paper we consider a fractional diffusion equation with a Riemann–Liouville derivative. The main objective is to investigate the convergence of solutions of the problem when the fractional order tends to <inline-formula...

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Bibliographic Details
Main Authors: Long Le Dinh, O’regan Donal
Format: Article
Language:English
Published: MDPI AG 2022-10-01
Series:Mathematics
Subjects:
fractional diffusion equation
Riemman–Liouville
regularity
convergence rate
Online Access:https://www.mdpi.com/2227-7390/10/21/4026
Description
Summary:Fractional diffusion equations have applications in various fields and in this paper we consider a fractional diffusion equation with a Riemann–Liouville derivative. The main objective is to investigate the convergence of solutions of the problem when the fractional order tends to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mn>1</mn><mo>−</mo></msup></semantics></math></inline-formula>. Under some suitable conditions on the Cauchy data, we prove the convergence results in a reasonable sense.
ISSN:2227-7390

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