in this paper a mathematical simulation of a simplified internal combustion engine is presented. to contribute engine kinematics and its geometry, simple relations are derived for constrained motions. the equation of motion for the piston forms a singular boundary value problem. the uniqueness of the solution was studied in the banach space. for solving governing equations an iterative numerica...

We study a special class of lower trigonometric matrix value boundary problems on hyperbolas. Firstly, the pseudo-orthogonal polynomial hyperbola is given in bilinear form and it shown that only one. Secondly, problem triangular presented transformed into four related problems. Finally, Liouville theorem Painlevé polynomials are used to give solutions.

In this paper, we prove the existence of the solution for boundary value prob-lem(BVP) of fractional dierential equations of order q 2 (2; 3]. The Kras-noselskii's xed point theorem is applied to establish the results. In addition,we give an detailed example to demonstrate the main result.