Abstract: In this article an evolutionary technique has been used
for the solution of nonlinear Riccati differential equations of fractional order. In this method, genetic algorithm is used as a tool for
the competent global search method hybridized with active-set algorithm for efficient local search. The proposed method has been
successfully applied to solve the different forms of Riccati
differential equations. The strength of proposed method has in its
equal applicability for the integer order case, as well as, fractional
order case. Comparison of the method has been made with standard
numerical techniques as well as the analytic solutions. It is found
that the designed method can provide the solution to the equation
with better accuracy than its counterpart deterministic approaches.
Another advantage of the given approach is to provide results on
entire finite continuous domain unlike other numerical methods
which provide solutions only on discrete grid of points.
Abstract: In this paper, some brief sufficient conditions for the stability of FO-LTI systems dαx(t) dtα = Ax(t) with the fractional order are investigated when the matrix A and the fractional order α are uncertain or both α and A are uncertain, respectively. In addition, we also relate the stability of a fractional-order system with order 0 < α ≤ 1 to the stability of its equivalent fractional-order system with order 1 ≤ β < 2, the relationship between α and β is presented. Finally, a numeric experiment is given to demonstrate the effectiveness of our results.
Abstract: In this work, we improve a previously developed
segmentation scheme aimed at extracting edge information from
speckled images using a maximum likelihood edge detector. The
scheme was based on finding a threshold for the probability density
function of a new kernel defined as the arithmetic mean-to-geometric
mean ratio field over a circular neighborhood set and, in a general
context, is founded on a likelihood random field model (LRFM). The
segmentation algorithm was applied to discriminated speckle areas
obtained using simple elliptic discriminant functions based on
measures of the signal-to-noise ratio with fractional order moments.
A rigorous stochastic analysis was used to derive an exact expression
for the cumulative density function of the probability density
function of the random field. Based on this, an accurate probability
of error was derived and the performance of the scheme was
analysed. The improved segmentation scheme performed well for
both simulated and real images and showed superior results to those
previously obtained using the original LRFM scheme and standard
edge detection methods. In particular, the false alarm probability was
markedly lower than that of the original LRFM method with
oversegmentation artifacts virtually eliminated. The importance of
this work lies in the development of a stochastic-based segmentation,
allowing an accurate quantification of the probability of false
detection. Non visual quantification and misclassification in medical
ultrasound speckled images is relatively new and is of interest to
clinicians.
Abstract: In this paper, we study the stability of a fractional order delayed predator-prey model. By using the Laplace transform, we introduce a characteristic equation for the above system. It is shown that if all roots of the characteristic equation have negative parts, then the equilibrium of the above fractional order predator-prey system is Lyapunov globally asymptotical stable. An example is given to show the effectiveness of the approach presented in this paper.