Application of Topological Degree Method for Solutions of Coupled Systems of Multipoints Boundary Value Problems of Fractional Order Hybrid Differential Equations
Joint Authors
Shah, Kamal
Iqbal, Muhammad
Khan, Rahmat Ali
Li, Yongjin
Source
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-07-20
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
We established the theory to coupled systems of multipoints boundary value problems of fractional order hybrid differential equations with nonlinear perturbations of second type involving Caputo fractional derivative.
The proposed problem is as follows: D cαxt-ft,xt=gt,yt,Iαyt, t∈J=[0,1],D cαyt-ft,yt=gt,xt,Iαxt, t∈J=0,1, D cpx0=ψxη1, x′0=0,…,xn-20=0, D cpx1=ψxη2, D cpy0=ψyη1, y′0=0,…,yn-20=0, D cpy1=ψyη2, where p,η1,η2∈0,1, ψ is linear, D cα is Caputo fractional derivative of order α, with n-1<α≤n, n∈N, and Iα is fractional integral of order α.
The nonlinear functions f, g are continuous.
For obtaining sufficient conditions on existence and uniqueness of positive solutions to the above system, we used the technique of topological degree theory.
Finally, we illustrated the main results by a concrete example.
American Psychological Association (APA)
Iqbal, Muhammad& Li, Yongjin& Shah, Kamal& Khan, Rahmat Ali. 2017. Application of Topological Degree Method for Solutions of Coupled Systems of Multipoints Boundary Value Problems of Fractional Order Hybrid Differential Equations. Complexity،Vol. 2017, no. 2017, pp.1-9.
https://search.emarefa.net/detail/BIM-1143430
Modern Language Association (MLA)
Iqbal, Muhammad…[et al.]. Application of Topological Degree Method for Solutions of Coupled Systems of Multipoints Boundary Value Problems of Fractional Order Hybrid Differential Equations. Complexity No. 2017 (2017), pp.1-9.
https://search.emarefa.net/detail/BIM-1143430
American Medical Association (AMA)
Iqbal, Muhammad& Li, Yongjin& Shah, Kamal& Khan, Rahmat Ali. Application of Topological Degree Method for Solutions of Coupled Systems of Multipoints Boundary Value Problems of Fractional Order Hybrid Differential Equations. Complexity. 2017. Vol. 2017, no. 2017, pp.1-9.
https://search.emarefa.net/detail/BIM-1143430
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1143430