We study a linear fractional differential equation with a periodic boundary condition and give the explicit form of the solution and the corresponding Green’s function. Using some properties of the Green’s function we present some new comparison results.

a simple, mild and high efficient procedure for one pot three component synthesis of 2-amino 4-h chromene derivatives was studied. the reaction was performed in water using aryl aldehydes, malononitrile and resorcinol, phloroglucinol or naphthole in the presence of n-methyl d-glucamine (meglumine) as a green high efficient catalyst. the reaction was studied in thermal, microwave (mw) and ultras...

this paper deals with the boundary value problem involving the differential equation ell y:=-y''+qy=lambda y, subject to the eigenparameter dependent boundary conditions along with the following discontinuity conditions y(d+0)=a y(d-0), y'(d+0)=ay'(d-0)+b y(d-0). in this problem q(x), d, a , b are real, qin l^2(0,pi), din(0,pi) and lambda is a parameter independent of x. by ...

the dynamic response of the railway under accelerated moving load using dynamic green function is presented in this paper. for this purpose, an exact and direct modeling technique is introduced for the railway modeling as the damped euler-bernoulli beam on the partial winkler foundation with arbitrary boundary conditions subjected to the moving load. the effects of the elastic coefficient of wi...

for the first time lactic acid was applied as an efficient and green catalyst for the one-pot three-component synthesis of amidoalkyl naphthols via the condensation between arylaldehydes, 2-naphthol and amides or urea under thermal solvent-free conditions in good to excellent yields. we have demonestrated a mild and efficient eco-friendly tandem synthesis of amidoalkyl naphthols using lactic ac...

This perspective on Tsao et al. (beginning on p. 931 in this issue of the journal) discusses green tea extract, which was shown for the first time to have dose-dependent effects in a clinical chemopreventive setting (oral premalignant lesions). This translational trial provides important data on angiogenesis and other biomarkers on which to base future clinical research, which should include tr...