Analysis of nonlinear fractional diffusion equations with a Riemann-liouville derivative

Tran Bao Ngoc; Nguyen Huy Tuan; R. Sakthivel; Donal O'Regan

doi:10.3934/eect.2021007

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2022, Volume 11, Issue 2: 439-455. Doi: 10.3934/eect.2021007

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Analysis of nonlinear fractional diffusion equations with a Riemann-liouville derivative

1.
Division of Applied Mathematics, Thu Dau Mot University, Binh Duong Province, Vietnam
2.
Faculty of Mathematics and Computer Science, University of Science, VNUHCM Ho Chi Minh City, Vietnam
3.
Department of Applied Mathematics, Bharathiar University, Coimbatore 641 046, India
4.
School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland

Corresponding author: Nguyen Huy Tuan (nguyenhuytuan@tdmu.edu.vn)
Corresponding author: Nguyen Huy Tuan (nguyenhuytuan@tdmu.edu.vn)

Received: May 2020

Revised: December 2020

Early access: January 2021

Published: April 2022

This paper is supported by Thu Dau Mot University. The authors wish to express their sincere thanks to the referees and the editor for their valuable comments

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Abstract

In this paper, we consider a nonlinear fractional diffusion equations with a Riemann-Liouville derivative. First, we establish the global existence and uniqueness of mild solutions under some assumptions on the input data. Some regularity results for the mild solution and its derivatives of fractional orders are also derived. Our key idea is to combine the theories of Mittag-Leffler functions, Banach fixed point theorem and some Sobolev embeddings.

Keywords:

Riemann-Liouville fractional derivative,
time diffusion equation,
well–posedness,
regularity estimates.

Mathematics Subject Classification: 26A33, 35B65, 35B05, 35R11.

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