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math.NA2026
Nonlinear fractional-periodic boundary value problems with Hilfer fractional derivative: existence and numerical approximations of solutions
Niels Goedegebure, Kateryna Marynets
We prove conditions for existence of analytical solutions for boundary value problems with the Hilfer fractional derivative, generalizing the commonly used Riemann-Liouville and Ca…
math.NA2025
A numerical Bernstein splines approach for nonlinear initial value problems with Hilfer fractional derivative
Niels Goedegebure, Kateryna Marynets
The Hilfer fractional derivative generalizes and interpolates between the commonly used Riemann-Liouville and Caputo fractional derivative. In general, solutions to Hilfer fraction…
math.NA2022★ 5 cited
Approximation approach to the fractional BVP with the Dirichlet type boundary conditions
Kateryna Marynets, Dona Pantova
We use a numerical-analytic technique to construct a sequence of successive approximations to the solution of a system of fractional differential equations, subject to Dirichlet bo…