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

AbstractA Lyapunov-type inequality is established for the anti-periodic fractional boundary value problem (CDaα,ψu)(x)+f(x,u(x))=0,a Click to show full abstract

AbstractA 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; anti periodic; periodic fractional; boundary value; fractional boundary; problem

Journal Title: Journal of Inequalities and Applications
Year Published: 2018

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