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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)

- Bashir Ahmad
- 2007

We apply the generalized quasilinearization technique to obtain a monotone sequence of iterates converging quadratically to the unique solution of a general second order nonlinear differential equation with nonlinear nonlocal mixed three-point boundary conditions. The convergence of order n (n ≥ 2) of the sequence of iterates has also been established.

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)

In this paper, we study the existence of solutions for a boundary value problem of differential inclusions of order q ∈ (1, 2] with non-separated boundary conditions involving convex and non-convex multivalued maps. Our results are based on the nonlinear alternative of Leray Schauder type and some suitable theorems of fixed point theory.

Complex valued linear algebraic systems arise in many important applications. We present analytical and extensive numerical comparisons of some available numerical solution methods. It is advocated, in particular for large scale ill-conditioned problems, to rewrite the complex-valued system in real valued form leading to a two-by-two block system of… (More)