Lyapunov-type inequalities for an anti-periodic fractional boundary value problem involving ψ-Caputo fractional derivative

摘要

A Lyapunov-type inequality is established for the anti-periodic fractional boundary value problem (CDaα,ψu)(x)+f(x,u(x))=0,a<x<b,u(a)+u(b)=0,u′(a)+u′(b)=0, where (a,b)∈R2, a<b, 1<α<2, ψ∈C2([a,b]), ψ′(x)>0, x∈[a,b], Daα,ψC is the ψ-Caputo fractional derivative of order α, and f:[a,b]×R→R is a given function. Next, we give an application of the obtained inequality to the corresponding eigenvalue problem.