The integer order model of dynamical system or biological system has a strict physical or biological meaning but if it is changed to fractional order what is the practical significance.
Fractional calculus is the theory that deals with the generalisation of
integral and derivative to a real or complex order. During the last decades, F.C
has gained popularity and importance due to its applications in diverse fi elds of sciences and engineering such as biology, physics, chemistry, engineering, control theory... . The advantages of fractional derivative is
that provide a powerful tool to model real process with long-rage memory,
long-rage interactions and hereditary properties wish exist in most biological systems, as opposed of integer derivative where such e ects are neglected
Spatial fractional derivative implies non-locality: the exterior domain cannot be decoupled from the exterior by conventional walls or boundary conditions. In theory it invalides all arguments based on surface to volume ratios becoming negligible in the thermodynamics limit. The story becomes clear when you deal with systems with long-range interaction. In general, the presence of long-range couplings in physical systems is reflected into the appearance of nonlocal terms in the continuum equations, the nonlocality being mathematically represented by spatial fractional derivatives....
1-) https://arxiv.org/pdf/1802.00247.pdf
2-)https://www.icp.uni-stuttgart.de/~hilfer/publikationen/pdfo/ZZ-2008-ATFaA-17.pdf
3-) Article Statistical Mechanics of systems with long range interactions
Since most of the biological systems have memory effect this only can be represented by fractional order which can easily verified by various literature
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