Abstract. Finding the symmetries of the nonlinear fractional di erential equations plays an important role in study of fractional di erential equations. In this manuscript, rstly, we are interested in nding the Lie point symmetries of the time-fractional KaupKupershmidt equation. Afterwards, by using the in nitesimal generators, we determine their corresponding invariant solutions.
Summary
The present study was conducted to evaluate the effects of dietary nucleotides (NT) on growth performance, immune responses, and intestinal morphology of striped catfish, Pangasianodon hypophthalmus. Different levels of NT (0, 0.25. 0.5, 0.75, and 1% weight per weight, WW−1) were used in the basal diet and then randomly allocated to triplicate groups of fish with an average initial weight of 1.52 ± 0.11 g for 10 weeks. Nucleotide supplementation did not improve growth parameters significantly (P > 0.05). Feeding fish with a NT‐containing diet significantly improved ACH50 activity and IgM levels in comparison to the control group (P < 0.05). The dietary NT (P < 0.05) affected the intestinal morphology, whereby the folds and enterocyte heights in the mid‐intestine were significantly increased compared to the control group (P < 0.05), while the microvilli length was not affected. The results indicate that feeding striped catfish with commercial NT have significant effects on the immune parameters and intestinal morphology of catfish and that the best NT levels are 0.25 and 0.5%.
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