In this paper we study polynomial maps of vector spaces zi → Ai1i2···is i zi1zi2zi3 · · · zis and their eigenvectors and eigenvalues. The new quantity called complanart is de ned. Complanarts determine complanarity of solution vectors of systems of polynomial equations. Evaluation of complanart is reduced to evaluation of resultants. As in linear case, the pattern of eigenvectors de nes the pha...

The Chapman-Kolmogorov equation with fractional integrals is derived. An integral of fractional order is considered as an approximation of the integral on fractal. Fractional integrals can be used to describe the fractal media. Using fractional integrals, the fractional generalization of the Chapman-Kolmogorov equation is obtained. From the fractional Chapman-Kolmogorov equation, the Fokker-Pla...

The Chapman–Kolmogorov equation with fractional integrals is derived. An integral of fractional order is considered as an approximation of the integral on fractal. Fractional integrals can be used to describe the fractal media. Using fractional integrals, the fractional generalization of the Chapman–Kolmogorov equation is obtained. From the fractional Chapman–Kolmogorov equation, the Fokker–Pla...

some preliminaries about the integrable families of riccati equations and solutions structure of these equations in several cases are presented in this paper, then by using of definitions for fractional derivative we apply the new extended of tanh method to the perturbed nonlinear fractional schrodinger equation with the kerr law nonlinearity. finally by using of this method and solutions of ri...

In this paper we discuss stochastic di erential delay equations with Markovian switching. Such an equation can be regarded 9 as the result of several stochastic di erential delay equations switching from one to another according to the movement of a Markov chain. The aim of this paper is to investigate the stability in distribution of the equations. 11 c © 2003 Published by Elsevier Science B.V.

The di erential equation dX dt X k X where k is a Toeplitz annihilator has been suggested as a means to solve the inverse Toeplitz eigenvalue problem Starting with the diagonal matrix whose entries are the same as the given eigenvalues the solution ow has been observed numerically to always converge a symmetric Toeplitz matrix as t This paper is an attempt to understand the dynamics involved in...

In this work, a non-integer order Airy equation involving Liouville differential operator is considered. Proposing an undetermined integral solution to the left fractional Airy differential equation, we utilize some basic fractional calculus tools to clarify the closed form. A similar suggestion to the right FADE, converts it into an equation in the Laplace domain. An illustration t...

The Haar wavelet collocation with iteration technique is applied for solving a class of time-fractional physical equations. The approximate solutions obtained by two dimensional Haar wavelet with iteration technique are compared with those obtained by analytical methods such as Adomian decomposition method (ADM) and variational iteration method (VIM). The results show that the present scheme is...

In this paper, a new fractional sub-equation method is proposed for finding exact solutions of fractional partial differential equations (FPDEs) in the sense of modified Riemann-Liouville derivative. With the aid of symbolic computation, we choose the space-time fractional Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZKBBM) equation in mathematical physics with a source to illustrate the validity a...