Electron. J. Differential Equations, Vol. 2023 (2023), No. 58, pp. 1-17.

Non-local fractional boundary value problems with applications to predator-prey models

Michal Feckan, Kateryna Marynets

We study a nonlinear fractional boundary value problem (BVP) subject to non-local multipoint boundary conditions. By introducing an appropriate parametrization technique we reduce the original problem to an equivalent one with already two-point restrictions. Using a notion of Chebyshev nodes and Lagrange polynomials we construct a successive iteration scheme, that converges to the exact solution of the non-local problem for particular values of the unknown parameters, which are calculated numerically.

Submitted February 23, 2023. Published September 11, 2023.
Math Subject Classifications: 34A08, 34K07, 34K28.
Key Words: Caputo derivative; non-local boundary conditions; Chebyshev nodes; approximation of solutions; Lagrange polynomial interpolation; predator-prey model.
DOI: 10.58997/ejde.2023.58

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Michal Feckan
Department of Mathematical Analysis and Numerical Analysis
Comenius University in Bratislava
Mlynska dolina, 842 48 Bratislava, Slovakia
email: michal.feckan@fmph.uniba.sk
Kateryna Marynets
Delft Institute of Applied Mathematics
Faculty of Electrical Engineering
Mathematics and Computer Science
Delft University of Technology
Mekelweg 4 2628CD Delft, Netherlands
email: K.Marynets@tudelft.nl

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