Successive approximations and interval halving for fractional BVPs with integral boundary conditions

• Published in: Journal of Computational and Applied Mathematics
• Main Authors: Marynets, K. (author), Pantova, D.H. (author)
• Format: Article in Journal/Newspaper
• Language: English
• Published: 2024
• Subjects: Approximation of solutions; Dichotomy-type approach; Fractional differential equations; Fractional geophysical model; Integral boundary conditions; Parametrization; Antarc*; Antarctic
• Online Access: http://resolver.tudelft.nl/uuid:eb661d08-fc10-4b5c-824d-72d68e00da85; https://doi.org/10.1016/j.cam.2023.115361

We study a system of non-linear fractional differential equations, subject to integral boundary conditions. We use a parametrization technique and a dichotomy-type approach to reduce the original problem to two “model-type” fractional boundary value problems with linear two-point boundary conditions. A numerical-analytic technique is applied to analytically construct approximate solutions to the “model-type” problems. The behaviour of these approximate solutions is governed by a set of parameters, whose values are obtained by numerically solving a system of algebraic equations. The obtained results are confirmed by an example of the fractional order problem that in the case of the second order differential equation models the Antarctic Circumpolar Current. Mathematical Physics