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.

in this paper, we prove the existence of fixed point for chatterjea type mappings under $c$-distance in cone metric spaces endowed with a graph. the main results extend, generalized and unified some fixed point theorems on $c$-distance in metric and cone metric spaces.

in this paper, we give some results on the common fixed point of self-mappings defined on complete $b$-metric spaces. our results generalize kannan and chatterjea fixed point theorems on complete $b$-metric spaces. in particular, we show that two self-mappings satisfying a contraction type inequality have a unique common fixed point. we also give some examples to illustrate the given results.

in this paper, we improve some recent coupled fixed point resultsfor single-valued operators in the framework of ordered $b$-metricspaces established by bota et al. [m-f. bota, a. petrusel, g.petrusel and b. samet, coupled fixed point theorems forsingle-valued operators in b-metric spaces, fixed point theoryappl. (2015) 2015:231]. also, we prove that perov-type fixed pointtheorem in ordered gen...

the time-optimal trajectory for an airplane from some starting point to some final point is studied by many authors. here, we consider the extension of robot planer motion of dubins model in three dimensional spaces. in this model, the system has independent bounded control over both the altitude velocity and the turning rate of airplane movement in a non-obstacle space. here, in this paper a g...

Let $M$ be an orientable hypersurface in the Euclidean space $R^{2n}$ with induced metric $g$ and $TM$ be its tangent bundle. It is known that the tangent bundle $TM$ has induced metric $overline{g}$ as submanifold of the Euclidean space $R^{4n}$ which is not a natural metric in the sense that the submersion $pi :(TM,overline{g})rightarrow (M,g)$ is not the Riemannian submersion. In this paper...