A boundary value problem with an integral condition for a certain fractional differential equation

The aim of this work is to prove the existence and the uniqueness of the solution of one dimensional initial boundary value problem for a parabolic equation with a Caputo time fractional differential operator supplemented by periodic nonlocal boundary condition and integral condition. First, an a pr...

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Bibliographic Details
Published inMathematical modelling and analysis Vol. 30; no. 3; pp. 405 - 420
Main Authors Hammou, Bouthina Sabah, Djerad, Abdelkader, Memou, Ameur, Latrous, Chahla
Format Journal Article
LanguageEnglish
Published Vilnius Gediminas Technical University 03.07.2025
Subjects
Caputo derivatives
energy inequality
fractional differential equation
integral boundary conditions
strong solution
fractional differential equation
integral boundary conditions
energy inequality
strong solution
Caputo derivatives
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Summary:The aim of this work is to prove the existence and the uniqueness of the solution of one dimensional initial boundary value problem for a parabolic equation with a Caputo time fractional differential operator supplemented by periodic nonlocal boundary condition and integral condition. First, an a priori estimate is established for the associated problem. Secondly, the density of the operator range generated by the considered problem is proved by using the functional analysis method.
ISSN:1392-6292
1648-3510
DOI:10.3846/mma.2025.21481