Lyapunov Type Inequality for an Anti-Periodic Conformable Boundary Value Problem

We consider a nonlinear fractional boundary value problem involving conformable variable-order derivative with Dirichlet conditions. We prove the existence of solutions to the considered problem by using the upper and lower solutions' method with Schauder's fixed-point theorem. In addition, under some assumptions on the nonlinear term, a new Lyapunov-type inequality is given for the corresponding boundary value problem. The obtained inequality provides a necessary condition for the existence of nontrivial solutions to the considered problem and a method to prove uniqueness for the nonhomogeneous boundary value problem. These new results are illustrated through examples.

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Green's function and an inequality of Lyapunov-type for conformable boundary value problem

Jonnalagadda

Băleanu

Basua

2020

Novi Sad J. Math.

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Lyapunov Type Inequality for an Anti-Periodic Conformable Boundary Value Problem

Abstract: In this article, we present a Lyapunov-type inequality for a conformable boundary value problem associated with anti-periodic boundary conditions. To demonstrate the applicability of established result, we obtain a lower bound on the eigenvalue of the corresponding eigenvalue problem.

Cited by 4 publications

References 17 publications

Lyapunov-Type Inequalities for Fractional Differential Operators with Non-singular Kernels

Lyapunov-Type Inequalities for Fractional Differential Operators with Non-singular Kernels

The existence of solutions for nonlinear fractional boundary value problem and its Lyapunov-type inequality involving conformable variable-order derivative

Green's function and an inequality of Lyapunov-type for conformable boundary value problem

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