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

Marynets, K.; Pantova, D.H.

doi:10.1016/j.cam.2023.115361

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

Title

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

Author

Marynets, K. (TU Delft Mathematical Physics)
Pantova, D.H. (TU Delft Mathematical Physics)

Date

2024

Abstract

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.

Subject

Approximation of solutions
Dichotomy-type approach
Fractional differential equations
Fractional geophysical model
Integral boundary conditions
Parametrization

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http://resolver.tudelft.nl/uuid:eb661d08-fc10-4b5c-824d-72d68e00da85

DOI

https://doi.org/10.1016/j.cam.2023.115361

ISSN

0377-0427

Source

Journal of Computational and Applied Mathematics, 436

Part of collection

Institutional Repository