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

Abstract

Abstract A Lyapunov-type inequality is established for the anti-periodic fractional boundary value problem (CDaα,ψu)(x)+f(x,u(x))=0,a0 $\psi'(x)>0$, x∈[a,b] $x\in[a,b]$, Daα,ψC ${}^{C}D_{a}^{\alpha,\psi}$ is the ψ-Caputo fractional derivative of order α, and f:[a,b]×R→R $f: [a,b]\times\mathbb{R}\to\mathbb{R}$ is a given function. Next, we give an application of the obtained inequality to the corresponding eigenvalue problem.

Keywords

• Lyapunov-type inequalities
• anti-periodic fractional boundary value problem
• ψ-Caputo fractional derivative
• eigenvalues