General fractional differential equations of order α∈ (1 , 2) and Type β∈ [0 , 1] in Banach spaces

Zhan Dong Mei; Ji Gen Peng; Jing Huai Gao

doi:10.1007/s00233-017-9859-4

General fractional differential equations of order α∈ (1 , 2) and Type β∈ [0 , 1] in Banach spaces

Zhan Dong Mei
, Ji Gen Peng
, Jing Huai Gao

Faculty of Electronic and Information Engineering

Xi'an Jiaotong University

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

10 Scopus citations

Abstract

In this paper, we are concerned with general fractional differential equations of order α∈ (1 , 2) and type β∈ [0 , 1] in Banach spaces. We define and develop a theory of general fractional sine functions and show that they are essentiality equivalent to a general fractional resolvent. We use such theory to study the well-posedness of the above general fractional differential equations. An illustration example is presented.

Original language	English
Pages (from-to)	712-737
Number of pages	26
Journal	Semigroup Forum
Volume	94
Issue number	3
DOIs	https://doi.org/10.1007/s00233-017-9859-4
State	Published - 1 Jun 2017

Keywords

Fractional differential equations
General fractional sine function
Mild solution
Strong solution

Access to Document

10.1007/s00233-017-9859-4

Cite this

@article{3dd1c1c1e3f34e2da013ed592782bfd4,

title = "General fractional differential equations of order α∈ (1 , 2) and Type β∈ [0 , 1] in Banach spaces",

abstract = "In this paper, we are concerned with general fractional differential equations of order α∈ (1 , 2) and type β∈ [0 , 1] in Banach spaces. We define and develop a theory of general fractional sine functions and show that they are essentiality equivalent to a general fractional resolvent. We use such theory to study the well-posedness of the above general fractional differential equations. An illustration example is presented.",

keywords = "Fractional differential equations, General fractional sine function, Mild solution, Strong solution",

author = "Mei, \{Zhan Dong\} and Peng, \{Ji Gen\} and Gao, \{Jing Huai\}",

note = "Publisher Copyright: {\textcopyright} 2017, Springer Science+Business Media New York.",

year = "2017",

month = jun,

day = "1",

doi = "10.1007/s00233-017-9859-4",

language = "英语",

volume = "94",

pages = "712--737",

journal = "Semigroup Forum",

issn = "0037-1912",

publisher = "Springer New York",

number = "3",

}

TY - JOUR

T1 - General fractional differential equations of order α∈ (1 , 2) and Type β∈ [0 , 1] in Banach spaces

AU - Mei, Zhan Dong

AU - Peng, Ji Gen

AU - Gao, Jing Huai

PY - 2017/6/1

Y1 - 2017/6/1

N2 - In this paper, we are concerned with general fractional differential equations of order α∈ (1 , 2) and type β∈ [0 , 1] in Banach spaces. We define and develop a theory of general fractional sine functions and show that they are essentiality equivalent to a general fractional resolvent. We use such theory to study the well-posedness of the above general fractional differential equations. An illustration example is presented.

AB - In this paper, we are concerned with general fractional differential equations of order α∈ (1 , 2) and type β∈ [0 , 1] in Banach spaces. We define and develop a theory of general fractional sine functions and show that they are essentiality equivalent to a general fractional resolvent. We use such theory to study the well-posedness of the above general fractional differential equations. An illustration example is presented.

KW - Fractional differential equations

KW - General fractional sine function

KW - Mild solution

KW - Strong solution

UR - https://www.scopus.com/pages/publications/85014510593

U2 - 10.1007/s00233-017-9859-4

DO - 10.1007/s00233-017-9859-4

M3 - 文章

AN - SCOPUS:85014510593

SN - 0037-1912

VL - 94

SP - 712

EP - 737

JO - Semigroup Forum

JF - Semigroup Forum

IS - 3

ER -

General fractional differential equations of order α∈ (1 , 2) and Type β∈ [0 , 1] in Banach spaces

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this