Existence and Uniqueness of Solution for a Class of Nonlinear Fractional Order Differential Equations
Joint Authors
Baleanu, Dumitru
Babakhani, Azizollah
Source
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-14, 14 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-06-26
Country of Publication
Egypt
No. of Pages
14
Main Subjects
Abstract EN
We discuss the existence and uniqueness of solution to nonlinear fractional order ordinary differential equations (Dα-ρtDβ)x(t)=f(t,x(t),Dγx(t)), t∈(0,1) with boundary conditions x(0)=x0, x(1)=x1 or satisfying the initial conditions x(0)=0, x′(0)=1, where Dα denotes Caputo fractional derivative, ρ is constant, 1<α<2, and 0<β+γ≤α.
Schauder's fixed-point theorem was used to establish the existence of the solution.
Banach contraction principle was used to show the uniqueness of the solution under certain conditions on f.
American Psychological Association (APA)
Babakhani, Azizollah& Baleanu, Dumitru. 2012. Existence and Uniqueness of Solution for a Class of Nonlinear Fractional Order Differential Equations. Abstract and Applied Analysis،Vol. 2012, no. 2012, pp.1-14.
https://search.emarefa.net/detail/BIM-486773
Modern Language Association (MLA)
Babakhani, Azizollah& Baleanu, Dumitru. Existence and Uniqueness of Solution for a Class of Nonlinear Fractional Order Differential Equations. Abstract and Applied Analysis No. 2012 (2012), pp.1-14.
https://search.emarefa.net/detail/BIM-486773
American Medical Association (AMA)
Babakhani, Azizollah& Baleanu, Dumitru. Existence and Uniqueness of Solution for a Class of Nonlinear Fractional Order Differential Equations. Abstract and Applied Analysis. 2012. Vol. 2012, no. 2012, pp.1-14.
https://search.emarefa.net/detail/BIM-486773
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-486773