Multiple Positive Solutions to Nonlinear Boundary Value Problems of a System for Fractional Differential Equations

Abstract EN

By using Krasnoselskii's fixed point theorem, we study the existence of at least one or two positive solutions to a system of fractional boundary value problems given by -D0+ν1y1(t)=λ1a1(t)f(y1(t),y2(t)), -D0+ν2y2(t)=λ2a2(t)g(y1(t),y2(t)), where D0+ν is the standard Riemann-Liouville fractional derivative, ν1,ν2∈(n-1,n] for n>3 and n∈N, subject to the boundary conditions y1(i)(0)=0=y2(i)(0), for 0≤i≤n-2, and [D0+αy1(t)]t=1=0=[D0+αy2(t)]t=1, for 1≤α≤n-2, or y1(i)(0)=0=y2(i)(0), for 0≤i≤n-2, and [D0+αy1(t)]t=1=ϕ1(y1), [D0+αy2(t)]t=1=ϕ2(y2), for 1≤α≤n-2, ϕ1,ϕ2∈C([0,1],R).

Our results are new and complement previously known results.

As an application, we also give an example to demonstrate our result.