In this paper the Bagley-Torvik equation as a prototype fractional differential equation with two derivatives is investigated by means of homotopy perturbation method. The results reveal that the present method is very effective and accurate.

We study Thurston’s Lipschitz and curve metrics, as well the arc metric on Teichmüller space of one-hold tori equipped with complete hyperbolic metrics boundary holonomy fixed length. construct natural maps between two surfaces such that generalize stretch prove following: (1) On torus one component, coincide define a geodesic this space. (2) same space, when length component is $$\le 4{\text {...

Diophantine approximation is traditionally the study of how well real numbers are approximated by rationals. We propose a model for studying in an arbitrary totally bounded metric space where rationals replaced with countable hierarchy “well-spread” points, which we refer to as abstract prove various Jarník–Besicovitch type dimension bounds and investigate their sharpness.