Abstract
In this paper, it is shown that a class of discrete Piece Wise Continuous (PWC) systems with Caputo-type delta fractional difference may not have solutions. To overcome this obstacle, the discontinuous problem is restarted as a continuous fractional problem. First, the single-valued PWC problem is transformed into a set-valued one via Filippov’s theory, after which Cellina’s theorem allows the restart of the problem into a single-valued continuous one. A numerical example is proposed and analyzed.
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