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Fractional boundary value problems on the half line

100%

Frioui A. , Guezane-Lakoud A. , Khaldi R.

Opuscula Mathematica

2017

tom Vol. 37, no. 2

265--280

In this paper, we focus on the solvability of a fractional boundary value problem at resonance on an unbounded interval. By constructing suitable operators, we establish an existence theorem upon the coincidence degree theory of Mawhin. The obtained results are illustrated by an example.

A new iteration method for the solution of third-order BVP via Green's function

72%

Akgun F. A. , Rasulov Z.

tom Vol. 54, nr 1

425--435

In this study, a new iterative method for third-order boundary value problems based on embedding Green’s function is introduced. The existence and uniqueness theorems are established, and necessary conditions are derived for convergence. The accuracy, efficiency and applicability of the results are demonstrated by comparing with the exact results and existing methods. The results of this paper extend and generalize the corresponding results in the literature.