Journal
SYMMETRY-BASEL
Volume 12, Issue 12, Pages -Publisher
MDPI
DOI: 10.3390/sym12121934
Keywords
2D system; conformable fractional derivative; CFD; Roesser model; general response formula
Categories
Funding
- National Science Centre in Poland [2017/27/B/ST7/02443]
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In many engineering problems associated with various physical phenomena, there occurs a necessity of analysis of signals that are described by multidimensional functions of more than one variable such as time t or space coordinates x, y, z. Therefore, in such cases, we should consider dynamical models of two or more dimensions. In this paper, a new two-dimensional (2D) model described by the Roesser type of state-space equations will be considered. In the introduced model, partial differential operators described by the Conformable Fractional Derivative (CFD) definition with respect to the first (horizontal) and second (vertical) variables will be applied. For the model under consideration, the general response formula is derived using the inverse fractional Laplace method. Next, the properties of the solution will be considered. Usefulness of the general response formula will be discussed and illustrated by a numerical example.
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