Open AccessAnalysis of nonlinear fractional diffusion equations with a Riemann-liouville derivative
Author(s) -
Tran Bao Ngoc,
Nguyen Huy Tuan,
R. Sakthivel,
Donal O’Regan
Publication year - 2022
Publication title -
evolution equations and control theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 19
eISSN - 2163-2480
pISSN - 2163-2472
DOI - 10.3934/eect.2021007
Subject(s) - uniqueness , mathematics , fractional calculus , nonlinear system , banach fixed point theorem , derivative (finance) , fixed point theorem , pure mathematics , sobolev space , mathematical analysis , mathematical physics , physics , quantum mechanics , financial economics , economics
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.