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

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...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2024-01, Vol.436, p.115361, Article 115361
Main Authors: Marynets, Kateryna, Pantova, Dona
Format: Article
Language:English
Subjects:
Approximation of solutions
Dichotomy-type approach
Fractional differential equations
Fractional geophysical model
Integral boundary conditions
Parametrization
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Summary: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.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2023.115361