Initial boundary value problems for space-time fractional conformable differential equation

In this paper, the authors study a initial boundary value problems (IBVP) for space-time fractional conformable partial differential equation (PDE). Several inequalities of fractional conformable derivatives at extremum points are presented and proved. Based on these inequalities at extremum points,...

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Bibliographic Details
Published inAIMS mathematics Vol. 6; no. 5; pp. 5275 - 5291
Main Authors Guan, Tingting, Wang, Guotao, Xu, Haiyong
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2021
Subjects
comparison theorem
maximum principle
space-time fractional conformable differential equation
uniqueness and continuous dependence
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Summary:In this paper, the authors study a initial boundary value problems (IBVP) for space-time fractional conformable partial differential equation (PDE). Several inequalities of fractional conformable derivatives at extremum points are presented and proved. Based on these inequalities at extremum points, a new maximum principle for the space-time fractional conformable PDE is demonstrated. Moreover, the maximum principle is employed to prove a new comparison principle and estimation of solutions. Beside that, the uniqueness and continuous dependence of the solution of the space-time fractional conformable PDE are demonstrated.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2021312