Positive solutions for fractional differential systems with nonlocal Riemann–Liouville fractional integral boundary conditions

In this paper, we study the positive solutions of fractional differential system with coupled nonlocal Riemann–Liouville fractional integral boundary conditions. Our analysis relies on Leggett–Williams and Guo–Krasnoselskii’s fixed point theorems. Two examples are worked out to illustrate our main results.     

Antimicrobial substances from the rare actinomycete Nonomuraea rhodomycinica NR4-ASC07T

Nonomuraea rhodomycinica NR4-ASC07^T is a rare actinomycete isolated from soil in Sirindhorn peat swamp forest. The crude extract of its culture broth exhibited antimicrobial and anticancer against diverse human pathogens and cancer cells. The chemical investigation of the crude extract led to the isolation of two new metabolites named nonomuric acid (1) and 3-hydroxy deoxydaunorubicinol aglycone (2), along with two known bioactive compounds [ε-rhodomycinone (3) and 7-deoxy-13-dihydrocarminomycinone (4)]. Compounds 1 and 3 showed antimalarial activity with the half maximal inhibitory concentration (IC₅₀) of 8.00 and 8.88 μg mL^?1, respectively. Compound 4 inhibited growth of Mycobacterium tuberculosis and Bacillus cereus at the minimum inhibitory concentrations of 50.0 and 12.50 μg mL^?1, respectively. Every compound exhibited cytotoxicity against cancer cells tested at IC₅₀ ≥ 6.34 μg mL^?1. These finding are the first report of bioactive metabolites produced by strain NR4-ASC07^T, suggesting that rare actinomycetes are yet promising sources for novel drug discovery.