This paper applies the Polynomial Least Squares Method (PLSM) to the case of fractional Lane-Emden differential equations. PLSM offers an analytical approximate polynomial solution in a straightforward way. A comparison with previously obtained results proves how accurate the method is.

In this paper, least squares homotopy perturbation is presented as a straightforward and accurate method to compute approximate analytical solutions for systems of ordinary differential equations. The method is employed to solve a problem related to a laminar flow of a viscous fluid in a semi-porous channel, which may be used to model the blood flow through a blood vessel, taking into account the effects of a magnetic field. The numerical computations show that the method is both easy to use and very accurate compared to the other methods previously used to solve the given problem.

In this paper a new method called the least squares differential quadrature method (LSDQM) is introduced as a straightforward and efficient method to compute analytical approximate polynomial solutions for nonlinear partial differential equations with fractional time derivatives. LSDQM is a combination of the differential quadrature method and the least squares method and in this paper it is employed to find approximate solutions for a very general class of nonlinear partial differential equations, wherein the fractional derivatives are described in the Caputo sense. The paper contains a clear, step-by-step presentation of the method and a convergence theorem. In order to emphasize the accuracy of LSDQM we included two test problems previously solved by means of other, well-known methods, and observed that our solutions present not only a smaller error but also a much simpler expression. We also included a problem with no known exact solution and the solutions computed by LSDQM are in good agreement with previous ones.

In this paper we apply the recently introduced Polynomial Least Squares Method (PLSM) to compute approximate analyticalpolynomial solutions for the Bagley-Torvik fractional equation with boundary conditions.The Bagley—Torvik equation may be used to model the motion of real physical systems such as the motion of a thin rigid plate immersed in a Newtonian fluid. In order to emphasize the accuracy of PLSM, we included a comparison with previous approximate solutions obtained for the Bagley-Torvik fractional equation by means of other approximation method.

Artificial intelligence (AI) provides a multitude of mechanisms that can be used to implement medical predictions systems. Even if this subject has been intensively debated during the last decades, choosing the most suitable mechanism is still a challenge. The research described in this paper focuses on stroke risk prediction and offers a tool meant to assist physicians in their decisions. Two consecrated methods are implemented (artificial neural networks and naive Bayesian classifier), and a comparison between them is provided. The results show that these methods have similar performances and can offer a valuable support for medical predictions.

In this paper an approach for computing an optimal control law based on the Polynomial Least Squares Method (PLSM) is presented. The initial optimal control problem is reformulated as a variational problem whose corresponding Euler-Lagrange equation is solved by using PLSM. A couple of examples emphasize the accuracy of the method.