Note on transport equation and fractional Sumudu transform.

In this paper, the Chebyshev polynomials to solve analytically the fractional neutron transport equation in one-dimensional plane geometry are used. The procedure is based on the expansion of the angular flux in terms of the Chebyshev polynomials. The obtained system of fractional linear differential equation is solved analytically by using fractional Sumudu transform

A Comparative Study of Shehu Variational Iteration Method and Shehu Decomposition Method for Solving Nonlinear Caputo Time-Fractional Wave-like Equations with Variable Coefficients

In this paper, a comparative study between two different methods for solving nonlinear Caputo time-fractional wave-like equations with variable coefficients is conducted. These two methods are called the Shehu variational iteration method (SVIM) and the Shehu decomposition method (SDM). To illustrate the efficiency and accuracy of the proposed methods, three different numerical examples are presented. The results obtained show that the two methods are powerful and efficient methods which both give approximations of higher accuracy and closed form solutions if existing. However, the SVIM has an advantage over SDM that it solves the nonlinear problems without using the Adomian polynomials. Furthermore, the SVIM enables us to overcome the difficulties arising in identifying the general Lagrange multiplier and it may be considered as an added advantage of this technique over the SDM

A New Method to Solve Fractional Differential Equations: Inverse Fractional Shehu Transform Method

In this paper, we propose a new method called the inverse fractional Shehu transform method to solve homogenous and non-homogenous linear fractional differential equations. Fractional derivatives are described in the sense of Riemann-Liouville and Caputo. Illustrative examples are given to demonstrate the validity, efficiency and applicability of the presented method. The solutions obtained by the proposed method are in complete agreement with the solutions available in the literature

Some Useful Collective Properties of Bessel, Marcum Q-Functions and Laguerre Polynomials

Special functions have been used widely in many problems of applied sciences. However, there are considerable numbers of problems in which exact solutions could not be achieved because of undefined sums or integrals involving special functions. These handicaps force researchers to seek new properties of special functions. Many problems that could not be solved so far would be solved by means of these efforts. Therefore in this article, we derived some useful properties and interrelations of each others of Bessel functions, Marcum Q-functions and Laguerre polynomials

Variational Iteration Method for a Fractional-Order Brusselator System

This paper presents approximate analytical solutions for the fractional-order Brusselator system using the variational iteration method. The fractional derivatives are described in the Caputo sense. This method is based on the incorporation of the correction functional for the equation. Two examples are solved as illustrations, using symbolic computation. The numerical results show that the introduced approach is a promising tool for solving system of linear and nonlinear fractional differential equations

Analytical solutions for the neutron transport using the spectral methods

We present a method for solving the two-dimensional equation of transfer. The method can be extended easily to the general linear transport problem. The used technique allows us to reduce the two-dimensional equation to a system of one-dimensional equations. The idea of using the spectral method for searching for solutions to the multidimensional transport problems leads us to a solution for all values of the independant variables, the proposed method reduces the solution of the multidimensional problems into a set of one-dimensional ones that have well-established deterministic solutions. The procedure is based on the development of the angular flux in truncated series of Chebyshev polynomials which will permit us to transform the two-dimensional problem into a set of one-dimensional problems

Etude de la structure topologique de l'ensemble des systèmes affines contrôlables en basse dimension

From a topological point of vien this work deals with the structure of a set of affine and controllable systems. From the work of (J.S.), (A.S.V.) it appeared that definite relations exist between topological structure of a set of affine controllable systems Ca and Ch. In particuler the properties of Fr Ca and the connexivy of Ca arise direcly from analogouds properties of Ch. We show that Ca gives rise to two types of boundary points. We can expect to have three types of boundary points. The interior of the closed set Ca contains affine controllable systems for which the trajectories are cycles. For the other cases they are on the exterior boundaries, we also show that the interior of Ca is uniquely composed of (J.S.) and affine controllable systems to which correspond homogeneous non-controllable systems characterized by collinear fields (non-independent spirals). Our result is that the set of affine controllable systems Ca is connectedCe travail traite du point de vue topologique la structure de l'ensemble des systèmes affines contrôlables. D'après les articles (J.S.), (A.S.V.) il est apparu des relations très fortes entre les structures topologiques de l'ensemble des systèmes affines contrôlables Ca et de Ch. En particulier les propriétés de FrCa et la connexité de Ca découlent directement de propriétés analogues pour Ch. On montre que Ca fait apparaitre deux types de points frontières où a priori il aurait pu y avoir trois types de points frontières. L'intérieur de sa fermeture contient les systèmes affines contrôlables pour lesquels les trajectoires sont des cycles, le restant des cas sont sur la frontière de son extérieur. On montre aussi que l'intérieur de Ca est constitué uniquement des (J.S.) et des systèmes affines contrôlables auxquels correspondent les systèmes homogènes non contrôlables caractérisés par les champs colinéaires (spirales liées). Notre résultat est que l'ensemble des systèmes affines contrôlables est connex