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Positive Solutions to Fractional Boundary Value Problems with Nonlinear Boundary Conditions
Joint Authors
Bashiri, Tahereh
Baleanu, Dumitru
Nyamoradi, Nemat
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-20, 20 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-06-24
Country of Publication
Egypt
No. of Pages
20
Main Subjects
Abstract EN
We consider a system of boundary value problems for fractional differential equation given by D0+βϕp(D0+αu)(t)=λ1a1(t)f1(u(t),v(t)), t∈(0,1), D0+βϕp(D0+αv)(t)=λ2a2(t)f2(u(t),v(t)), t∈(0,1), where 1<α, β≤2, 2<α+β≤4, λ1, λ2 are eigenvalues, subject either to the boundary conditions D0+αu(0)=D0+αu(1)=0, u(0)=0, D0+β1u(1)-Σi=1m-2a1i D0+β1u(ξ1i)=0, D0+αv(0)=D0+αv(1)=0, v(0)=0, D0+β1v(1)-Σi=1m-2a2i D0+β1v(ξ2i)=0 or D0+αu(0)=D0+αu(1)=0, u(0)=0, D0+β1u(1)-Σi=1m-2a1i D0+β1u(ξ1i)=ψ1(u), D0+αv(0)=D0+αv(1)=0, v(0)=0, D0+β1v(1)-Σi=1m-2a2i D0+β1v(ξ2i)=ψ2(v), where 0<β1<1, α-β1-1≥0 and ψ1, ψ2:C([0,1])→[0, ∞) are continuous functions.
The Krasnoselskiis fixed point theorem is applied to prove the existence of at least one positive solution for both fractional boundary value problems.
As an application, an example is given to demonstrate some of main results.
American Psychological Association (APA)
Nyamoradi, Nemat& Baleanu, Dumitru& Bashiri, Tahereh. 2013. Positive Solutions to Fractional Boundary Value Problems with Nonlinear Boundary Conditions. Abstract and Applied Analysis،Vol. 2013, no. 2013, pp.1-20.
https://search.emarefa.net/detail/BIM-482353
Modern Language Association (MLA)
Nyamoradi, Nemat…[et al.]. Positive Solutions to Fractional Boundary Value Problems with Nonlinear Boundary Conditions. Abstract and Applied Analysis No. 2013 (2013), pp.1-20.
https://search.emarefa.net/detail/BIM-482353
American Medical Association (AMA)
Nyamoradi, Nemat& Baleanu, Dumitru& Bashiri, Tahereh. Positive Solutions to Fractional Boundary Value Problems with Nonlinear Boundary Conditions. Abstract and Applied Analysis. 2013. Vol. 2013, no. 2013, pp.1-20.
https://search.emarefa.net/detail/BIM-482353
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-482353