Fractional periodic boundary value and Cauchy problems with Hilfer–Prabhakar operator
Kateryna Marynets (TU Delft - Mathematical Physics)
Živorad Tomovski (Palacky University, University of Ostrava)
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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.
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