Abstract: In this paper, we apply the shifted Legendre polynomial method (SLPM) to solve the fractional Volterra’s model for population growth of a species in a closed system. The SLPM solution procedure for nonlinear fractional integro-differential equations is established. Moreover, the accurate analytical approximations are obtained, which are valid and convergent for different fractional or...

In this paper we propose, a collocation method for solving nonlinear singular Lane-Emden equation which is a nonlinear ordinary differential equation on semi-infnite interval. This approach is based on a generalized Laguerre polynomial collocation method. This method reduces the solution of this problem to the solution of a system of algebraic equations.We also present the comparison of this wo...

Abstract: In the present article, a semi-analytical technique to investigate free bending vibration behavior of axially functionally graded non-prismatic Timoshenko beam subjected to a point force at both ends is developed based on the power series expansions. The beam is assumed to be made of linear elastic and isotropic material with constant Poisson ratio. Material properties including the ...

Abstract Butterfly wings are closely related to the premature failure of rolling element bearings. In this study, butterfly formation is investigated using developed semi-analytical three-dimensional (3D) contact model incorporating inclusion and material property degradation. The 3D elastic field introduced by inhomogeneous solved numerical approaches, which include equivalent method (EIM) con...

We consider nondeterministic probabilistic programs with the most basic liveness property of termination. We present efficient methods for termination analysis of nondeterministic probabilistic programs with polynomial guards and assignments. Our approach is through synthesis of polynomial ranking supermartingales, that on one hand significantly generalizes linear ranking supermartingales and o...

This paper proposes a novel approach for analyzing the stability of polynomial fractional-order systems using frequency-distributed fractional integrator model. There are two types frequency and temporal stabilization methods that global semi-global conditions attain sum-of-squares (SOS) method. Substantiation asymptotical complicated systems. According to recent studies on nonlinear systems, t...