In this article, a Legendre wavelet-Chebyshev wavelet spectral collocation method is proposed for solving fractional order space-time Burger's equation with the Legendre wavelet and Chebyshev wavelet operational matrices of fractional derivatives. The fractional derivative is described in the Caputo sense. The proposed method is based on Legendre wavelet-Chebyshev wavelet for space and time variables respectively. This method will reduc the problem under consideration to the solution of nonlinear algebraic equations. In order to confirm the efficiency of the proposed method, two numerical examples are implemented and comparing the numerical solution with the exact one, as well as, of other methods in given literatures, we demonstrate the high accuracy and efficiency of the proposed method.
The local existence and uniqueness of S-classical solution (semi-classical solution) for a class of semilinear initial value control problems in suitable Banach spaces have been discussed and proved. The theoretical results are depending on the theory of analytic semigroup and Banach contraction principle.Keywords: S-classical solution (semi-classical solution), control problem in infinite dimensional spaces, fixed point theorem and analytic semigroup theory.
This paper aims to apply the Bees Algorithm for solving system of equations. The solving System of Equations may be linear or nonlinear for a number of unknowns. As an application of System of Equations, we can implement cryptanalysis attack algorithms on stream cipher systems using plaintext attack (or part from it). We consider the Geffe System (which has nonlinear combining function) to be our study case, which is depend on set of Linear Feedback Shift Registers, as a model of stream cipher systems, in the performance of Bees Algorithm by solving System of Equations for any number of variables of the output of Linear Feedback Shift Registers. The application divided into two stages, first, constructing System of Equations for the suggested cryptosystem, and the second, is attacking the variables of System of Equations which they are also represent the initial key values of the combined of Linear Feedback Shift Registers.
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