Critical exponents of Fujita type for certain evolution equations and systems with spatio-temporal fractional derivatives

M. Kirane; Y. Laskri; N. E. Tatar

doi:10.1016/j.jmaa.2005.03.054

Critical exponents of Fujita type for certain evolution equations and systems with spatio-temporal fractional derivatives

M. Kirane^*
, Y. Laskri
, N. E. Tatar

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

119 Scopus citations

Abstract

This paper is concerned with establishing necessary or sufficient conditions for the existence of solutions to evolution equations with fractional derivatives in space and time. The Fujita exponent is determined. Then, these results are extended to systems of reaction-diffusion equations. Our new results shed lights on important practical questions.

Original language	English
Pages (from-to)	488-501
Number of pages	14
Journal	Journal of Mathematical Analysis and Applications
Volume	312
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2005.03.054
State	Published - 15 Dec 2005

Bibliographical note

Funding Information:
The third author expresses his gratitude to King Fahd University of Petroleum and Minerals for its financial support.

Keywords

Fractional derivatives
Fujita's exponent
Nonlinear evolution equations
Nonlinear reaction-diffusion systems
Porous media

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2005.03.054

Cite this

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title = "Critical exponents of Fujita type for certain evolution equations and systems with spatio-temporal fractional derivatives",

abstract = "This paper is concerned with establishing necessary or sufficient conditions for the existence of solutions to evolution equations with fractional derivatives in space and time. The Fujita exponent is determined. Then, these results are extended to systems of reaction-diffusion equations. Our new results shed lights on important practical questions.",

keywords = "Fractional derivatives, Fujita's exponent, Nonlinear evolution equations, Nonlinear reaction-diffusion systems, Porous media",

author = "M. Kirane and Y. Laskri and Tatar, \{N. E.\}",

note = "Funding Information: The third author expresses his gratitude to King Fahd University of Petroleum and Minerals for its financial support.",

year = "2005",

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doi = "10.1016/j.jmaa.2005.03.054",

language = "English",

volume = "312",

pages = "488--501",

journal = "Journal of Mathematical Analysis and Applications",

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T1 - Critical exponents of Fujita type for certain evolution equations and systems with spatio-temporal fractional derivatives

AU - Kirane, M.

AU - Laskri, Y.

AU - Tatar, N. E.

N1 - Funding Information: The third author expresses his gratitude to King Fahd University of Petroleum and Minerals for its financial support.

PY - 2005/12/15

Y1 - 2005/12/15

N2 - This paper is concerned with establishing necessary or sufficient conditions for the existence of solutions to evolution equations with fractional derivatives in space and time. The Fujita exponent is determined. Then, these results are extended to systems of reaction-diffusion equations. Our new results shed lights on important practical questions.

AB - This paper is concerned with establishing necessary or sufficient conditions for the existence of solutions to evolution equations with fractional derivatives in space and time. The Fujita exponent is determined. Then, these results are extended to systems of reaction-diffusion equations. Our new results shed lights on important practical questions.

KW - Fractional derivatives

KW - Fujita's exponent

KW - Nonlinear evolution equations

KW - Nonlinear reaction-diffusion systems

KW - Porous media

UR - https://www.scopus.com/pages/publications/27744500223

U2 - 10.1016/j.jmaa.2005.03.054

DO - 10.1016/j.jmaa.2005.03.054

M3 - Article

AN - SCOPUS:27744500223

SN - 0022-247X

VL - 312

SP - 488

EP - 501

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Critical exponents of Fujita type for certain evolution equations and systems with spatio-temporal fractional derivatives

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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