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

Tingting Guan; Guotao Wang; Haiyong Xu; Tingting Guan; Guotao Wang; Haiyong Xu

doi:10.3934/math.2021312

AIMS Mathematics

2021, Volume 6, Issue 5: 5275-5291. doi: 10.3934/math.2021312

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

1.
School of Mathematics and Computer Science, Shanxi Normal University, Linfen, Shanxi 041004, China
2.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan, China
3.
School of Mathematics and Statistics, Ningbo University, Ningbo 315212, China

Received: 06 January 2021 Accepted: 28 February 2021 Published: 12 March 2021
MSC : 26A33, 35K55

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.
- space-time fractional conformable differential equation,
- maximum principle,
- comparison theorem,
- uniqueness and continuous dependence
Citation: Tingting Guan, Guotao Wang, Haiyong Xu. Initial boundary value problems for space-time fractional conformable differential equation[J]. AIMS Mathematics, 2021, 6(5): 5275-5291. doi: 10.3934/math.2021312

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Abstract

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.

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