Nonlinear Fractional Boundary Value Problems: Existence Results and Approximation of Solutions
D.H. Pantova (TU Delft - Electrical Engineering, Mathematics and Computer Science)
H.M. Schuttelaars – Promotor (TU Delft - Electrical Engineering, Mathematics and Computer Science)
J.L.A. Dubbeldam – Promotor (TU Delft - Electrical Engineering, Mathematics and Computer Science)
K. Marynets – Copromotor (TU Delft - Electrical Engineering, Mathematics and Computer Science)
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Abstract
In this thesis, we develop constructive methods for the approximation of solutions to nonlinear boundary value problems (BVPs) in the fractional setting, subject to different types of boundary conditions. The main problems considered are: the solvability analysis and approximation of solutions of fractional BVPs with two-point and integral boundary conditions; the constructive approximations and monotonicity behavior of solutions of fractional BVPs with parameter-dependent right-hand sides; and the solvability analysis and approximation of solutions of fractional BVPs with parameter-dependent boundary conditions and a boundary condition at infinity. The theoretical results are supported by illustrative examples.