The existence of mild and classical solutions for a second-order abstract fractional problem

Nasser Eddine Tatar

doi:10.1016/j.na.2010.06.085

The existence of mild and classical solutions for a second-order abstract fractional problem

Nasser Eddine Tatar^*

^*Corresponding author for this work

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

7 Scopus citations

Abstract

In this paper we consider a second-order abstract problem involving derivatives of non-integer order. The existence and uniqueness of mild and classical solutions are established in appropriate spaces under weak assumptions.

Original language	English
Pages (from-to)	3130-3139
Number of pages	10
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	73
Issue number	9
DOIs	https://doi.org/10.1016/j.na.2010.06.085
State	Published - 1 Nov 2010

Bibliographical note

Funding Information:
The author is very grateful for the financial support provided by King Fahd University of Petroleum and Minerals through the Grant No. IP 091010 .

Keywords

Cauchy problem
Cosine family
Fractional derivative
Mild solutions
Second-order abstract problem

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.na.2010.06.085

Cite this

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title = "The existence of mild and classical solutions for a second-order abstract fractional problem",

abstract = "In this paper we consider a second-order abstract problem involving derivatives of non-integer order. The existence and uniqueness of mild and classical solutions are established in appropriate spaces under weak assumptions.",

keywords = "Cauchy problem, Cosine family, Fractional derivative, Mild solutions, Second-order abstract problem",

author = "Tatar, \{Nasser Eddine\}",

note = "Funding Information: The author is very grateful for the financial support provided by King Fahd University of Petroleum and Minerals through the Grant No. IP 091010 .",

year = "2010",

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day = "1",

doi = "10.1016/j.na.2010.06.085",

language = "English",

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journal = "Nonlinear Analysis, Theory, Methods and Applications",

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T1 - The existence of mild and classical solutions for a second-order abstract fractional problem

AU - Tatar, Nasser Eddine

N1 - Funding Information: The author is very grateful for the financial support provided by King Fahd University of Petroleum and Minerals through the Grant No. IP 091010 .

PY - 2010/11/1

Y1 - 2010/11/1

N2 - In this paper we consider a second-order abstract problem involving derivatives of non-integer order. The existence and uniqueness of mild and classical solutions are established in appropriate spaces under weak assumptions.

AB - In this paper we consider a second-order abstract problem involving derivatives of non-integer order. The existence and uniqueness of mild and classical solutions are established in appropriate spaces under weak assumptions.

KW - Cauchy problem

KW - Cosine family

KW - Fractional derivative

KW - Mild solutions

KW - Second-order abstract problem

UR - https://www.scopus.com/pages/publications/77955657759

U2 - 10.1016/j.na.2010.06.085

DO - 10.1016/j.na.2010.06.085

M3 - Article

AN - SCOPUS:77955657759

SN - 0362-546X

VL - 73

SP - 3130

EP - 3139

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 9

ER -

The existence of mild and classical solutions for a second-order abstract fractional problem

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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