The Existence of Positive Solutions for a New Coupled System of Multiterm Singular Fractional Integrodifferential Boundary Value Problems

• Main Authors: Dumitru Baleanu, Sayyedeh Zahra Nazemi, Shahram Rezapour
• Format: Article
• Language: English
• Published: Hindawi Limited 2013-01-01
• Series: Abstract and Applied Analysis
• Online Access: http://dx.doi.org/10.1155/2013/368659

We discuss the existence of positive solutions for the coupled system of multiterm singular fractional integrodifferential boundary value problems D0+αu(t)+f1(t,u(t),v(t),(ϕ1u)(t),(ψ1v)(t),D0+pu(t),D0+μ1v(t),D0+μ2v(t),…,D0+μmv(t))=0,D0+βv(t)+f2(t,u(t),v(t),(ϕ2u)(t),(ψ2v)(t),D0+qv(t),D0+ν1u(t),D0+ν2u(t),…,D0+νmu(t))=0, u(i)(0)=0 and v(i)(0)=0 for all 0≤i≤n-2, [D0+δ1u(t)]t=1=0 for 2<δ1<n-1 and α-δ1≥1, [D0+δ2v(t)]t=1=0 for 2<δ2<n-1 and β-δ2≥1, where n≥4, n-1<α,β<n, 0<p,q<1, 1<μi,νi<2  (i=1,2,…,m), γj,λj:[0,1]×[0,1]→(0,∞) are continuous functions (j=1,2) and (ϕju)(t)=∫0t‍γj(t,s)u(s)ds,(ψjv)(t)=∫0t‍λj(t,s)v(s)ds. Here D is the standard Riemann-Liouville fractional derivative, fj  (j=1,2) is a Caratheodory function, and fj(t,x,y,z,w,v,u1,u2,…,um) is singular at the value 0 of its variables.