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

ANALYSIS OF NONLINEAR FRACTIONAL DIFFUSION EQUATIONS WITH A RIEMANN-LIOUVILLE DERIVATIVE

Tran Bao Ngoc, Nguyen Huy Tuan, R. Sakthivel, Donal O’regan

Mathematics

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

1 Citation (Scopus)

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.

Original language	English
Pages (from-to)	439-455
Number of pages	17
Journal	Evolution Equations and Control Theory
Volume	11
Issue number	2
DOIs	https://doi.org/10.3934/eect.2021007
Publication status	Published - Apr 2022

Keywords

Regularity estimates
Riemann-Liouville fractional derivative
Time diffusion equation
Well–posedness

Access to Document

10.3934/eect.2021007

Cite this

@article{135f4a843a13457a842315ed62298c7b,

title = "ANALYSIS OF NONLINEAR FRACTIONAL DIFFUSION EQUATIONS WITH A RIEMANN-LIOUVILLE DERIVATIVE",

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 = "Regularity estimates, Riemann-Liouville fractional derivative, Time diffusion equation, Well–posedness",

author = "Ngoc, \{Tran Bao\} and Tuan, \{Nguyen Huy\} and R. Sakthivel and Donal O{\textquoteright}regan",

year = "2022",

month = apr,

doi = "10.3934/eect.2021007",

language = "English",

volume = "11",

pages = "439--455",

journal = "Evolution Equations and Control Theory",

issn = "2163-2472",

publisher = "American Institute of Mathematical Sciences",

number = "2",

}

TY - JOUR

T1 - ANALYSIS OF NONLINEAR FRACTIONAL DIFFUSION EQUATIONS WITH A RIEMANN-LIOUVILLE DERIVATIVE

AU - Ngoc, Tran Bao

AU - Tuan, Nguyen Huy

AU - Sakthivel, R.

AU - O’regan, Donal

PY - 2022/4

Y1 - 2022/4

N2 - 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.

AB - 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.

KW - Regularity estimates

KW - Riemann-Liouville fractional derivative

KW - Time diffusion equation

KW - Well–posedness

UR - https://www.scopus.com/pages/publications/85123535697

U2 - 10.3934/eect.2021007

DO - 10.3934/eect.2021007

M3 - Article

AN - SCOPUS:85123535697

SN - 2163-2472

VL - 11

SP - 439

EP - 455

JO - Evolution Equations and Control Theory

JF - Evolution Equations and Control Theory

IS - 2

ER -

ANALYSIS OF NONLINEAR FRACTIONAL DIFFUSION EQUATIONS WITH A RIEMANN-LIOUVILLE DERIVATIVE

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this