Abstract
We introduce a successive approximations method to study one fractional periodic boundary value problem of the Hilfer-Prabhakar type. The problem is associated to the corresponding Cauchy problem, whose solution depends on an unknown initial value. To find this value we numerically solve the so-called ’determining system’ of algebraic or transcendental equations. As a result, we determine an approximate solution of the studied problem, written in a closed form. Finally, we evaluate efficiency of our method on a nonlinear numerical example.
Original language | English |
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Article number | 130 |
Number of pages | 20 |
Journal | Computational and Applied Mathematics |
Volume | 43 |
Issue number | 3 |
DOIs | |
Publication status | Published - 2024 |
Keywords
- Cauchy problem
- Determining system
- Hilfer–Prabhakar fractional derivative
- Periodic boundary conditions
- Successive approximations