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

• Published in: AIMS mathematics Vol. 6; no. 5; pp. 5275 - 5291
• Main Authors: Guan, Tingting, Wang, Guotao, Xu, Haiyong
• Format: Journal Article
• Language: English
• Published: AIMS Press 01.01.2021
• Subjects: comparison theorem; maximum principle; space-time fractional conformable differential equation; uniqueness and continuous dependence
• ISSN: 2473-6988; 2473-6988
• DOI: 10.3934/math.2021312

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.