학술논문
Fractional periodic boundary value and Cauchy problems with Hilfer–Prabhakar operator
Document Type
Original Paper
Author
Source
Computational and Applied Mathematics. 43(3)
Subject
Language
English
ISSN
2238-3603
1807-0302
1807-0302
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.