No abstract

In this paper, we prove the existence of solutions for a boundary value problem involving both left Riemann-Liouville and right Caputo-type fractional derivatives. For this, we convert the posed problem to a sum of two integral operators, then we apply Krasnoselskii's fixed point theorem to conclude the existence of nontrivial solutions.

We derive a new Lyapunov type inequality for a boundary value problem involving both left Riemann-Liouville and right Caputo fractional derivatives in presence of natural conditions. Application to the corresponding eigenvalue problem is also discussed.

No abstract

We consider a boundary value problem involving conformable derivative of order α, 1 < α < 2 and Dirichlet conditions. To prove the existence of solutions, we apply the method of upper and lower solutions together with Schauder's fixed-point theorem. Futhermore, we give the Lyapunov inequality for the corresponding problem.