Mild solutions for a problem involving fractional derivatives in the nonlinearity and in the non-local conditions

Nasser Eddine Tatar

doi:10.1186/1687-1847-2011-18

Mild solutions for a problem involving fractional derivatives in the nonlinearity and in the non-local conditions

Nasser Eddine Tatar^*

^*Corresponding author for this work

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

6 Scopus citations

Abstract

A second-order abstract problem of neutral type with derivatives of non-integer order in the nonlinearity as well as in the nonlocal conditions is investigated. This model covers many of the existing models in the literature. It extends the integer order case to the fractional case in the sense of Caputo. A fixed point theorem is used to prove existence of mild solutions.

Original language	English
Article number	18
Journal	Advances in Difference Equations
Volume	2011
DOIs	https://doi.org/10.1186/1687-1847-2011-18
State	Published - 2011

Bibliographical note

Funding Information:
The author is very grateful for the financial support provided by King Fahd University of Petroleum and Minerals through the project No. IN 100007.

Keywords

Cauchy problem
Cosine family
Fractional derivative
Mild solutions
Neutral second-order abstract problem

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Applied Mathematics

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10.1186/1687-1847-2011-18

Cite this

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title = "Mild solutions for a problem involving fractional derivatives in the nonlinearity and in the non-local conditions",

abstract = "A second-order abstract problem of neutral type with derivatives of non-integer order in the nonlinearity as well as in the nonlocal conditions is investigated. This model covers many of the existing models in the literature. It extends the integer order case to the fractional case in the sense of Caputo. A fixed point theorem is used to prove existence of mild solutions.",

keywords = "Cauchy problem, Cosine family, Fractional derivative, Mild solutions, Neutral 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 project No. IN 100007. ",

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language = "English",

volume = "2011",

journal = "Advances in Difference Equations",

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T1 - Mild solutions for a problem involving fractional derivatives in the nonlinearity and in the non-local conditions

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 project No. IN 100007.

PY - 2011

Y1 - 2011

N2 - A second-order abstract problem of neutral type with derivatives of non-integer order in the nonlinearity as well as in the nonlocal conditions is investigated. This model covers many of the existing models in the literature. It extends the integer order case to the fractional case in the sense of Caputo. A fixed point theorem is used to prove existence of mild solutions.

AB - A second-order abstract problem of neutral type with derivatives of non-integer order in the nonlinearity as well as in the nonlocal conditions is investigated. This model covers many of the existing models in the literature. It extends the integer order case to the fractional case in the sense of Caputo. A fixed point theorem is used to prove existence of mild solutions.

KW - Cauchy problem

KW - Cosine family

KW - Fractional derivative

KW - Mild solutions

KW - Neutral second-order abstract problem

UR - https://www.scopus.com/pages/publications/84868110263

U2 - 10.1186/1687-1847-2011-18

DO - 10.1186/1687-1847-2011-18

M3 - Article

AN - SCOPUS:84868110263

SN - 1687-1839

VL - 2011

JO - Advances in Difference Equations

JF - Advances in Difference Equations

M1 - 18

ER -

Mild solutions for a problem involving fractional derivatives in the nonlinearity and in the non-local conditions

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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