The sufficient conditions are established for the existence of solutions for a class of boundary value problems for fractional differential equations involving the Caputo fractional derivative.

The authors investigate the existence of solutions to a class of boundary value problems for fractional q-difference equations in a Banach space that involves a q-derivative of the Caputo type and nonlinear integral boundary conditions. Their result is based on Mönch’s fixed point theorem and the technique of measures of noncompactness. This approach has proved to be an interesting and useful approach to studying such problems. Some basic concepts from the fractional q-calculus are introduced, including q-derivatives and q-integrals. An example of the main result is included as well as some suggestions for future research.

This study aimed to evaluate the prevalence of anti-West Nile virus (WNV) IgG among two populations of Tunisian blood donors living in areas where human outbreaks of WNV have occurred. Cohorts A (Monastir) and B (Mahdia) included 742 and 102 blood donors respectively. Sera were tested by IgG ELISA test and results were confirmed by PRNT test. WNV neutralizing antibodies were detected in 32 (4.3%) and in 14 (13.7%) sera in cohorts A and B respectively. The prevalence of anti-WNV IgG was significantly higher in cohort B than in cohort A (P<0.001) and was significantly lower in females than in males (P<0.001).

The authors establish sufficient conditions for the existence of solutions to boundary value problems for fractional differential inclusions involving the Hadamard type fractional derivative of order $\alpha \in (1,2]$ in Banach spaces. Their approach uses M\"onch's fixed point theorem and the Kuratowski measure of noncompacteness.