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

Abstract EN

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

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.