Electronic Journal of Differential Equations, Vol. 2023 (2023), No. 58, pp. 1-17.

Title: Non-local fractional boundary value problems with applications to predator-prey models
       
Authors: Michal Feckan (Comenius Univ. in Bratislava, Mlynska dolina, Slovakia)
         Kateryna Marynets (Delft Univ. of Technology, Netherlands)
         
Abstract: 
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.