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This paper studies a coupled system of nonlinear fractional differential equation with three-point boundary conditions. Applying the Schauder fixed point theorem, an existence result is proved for the following system D α u (t) = f (t, v (t) , D m v (t)) , t ∈ (0, 1) , D β v (t) = g (t, u (t) , D n u (t)) , t ∈ (0, 1) , u (0) = 0, D θ u (1) = δD θ u (η) , v… (More)

We discuss the existence of positive solutions of a nonlinear nth order boundary value problem u (n) + a(t) f (u) = 0, t ∈ (0, 1) u(0) = 0, u (n−2) (0) = 0, αu(η) = u(1), where 0 < η < 1, 0 < αη n−1 < 1. In particular, we establish the existence of at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem in… (More)

In the original Virtual Element space with degree of accuracy k, projector operators in the H 1-seminorm onto polynomials of degree ≤ k can be easily computed. On the other hand, projections in the L 2 norm are available only on polynomials of degree ≤ k − 2 (directly from the degrees of freedom). Here we present a variant of VEM that allows the exact… (More)

MSC: 34A08 34B15 34B40 45J05 Keywords: Nonlinear fractional integro-differential equations Banach space Explicit iterative sequence Error estimate Infinite interval a b s t r a c t In this paper, by employing the fixed point theory and the monotone iterative technique, we investigate the existence of a unique solution for a class of nonlinear fractional… (More)

This paper is concerned with the event-triggered distributed state estimation problem for a class of uncertain stochastic systems with state-dependent noises and randomly occurring uncertainties (ROUs) over sensor networks. An event-triggered communication scheme is proposed in order to determine whether the measurements on each sensor should be transmitted… (More)