The presented work includes the Homotopy Transforms of Analysis Method (HTAM). By this method, the approximate solution of nonlinear Navier- Stokes equations of fractional order derivative was obtained.  The Caputo's derivative was used in the proposed method. The desired solution was calculated by using the convergent power series to the components. The obtained results are demonstrated by comparison with the results of Adomain decomposition method, Homotopy Analysis method and exact solution, as explained in examples (4.1) and (4.2). The comparison shows that the used method is powerful and efficient.

This paper introduces the Multistep Modified Reduced Differential Transform Method (MMRDTM). It is applied to approximate the solution for Nonlinear Schrodinger Equations (NLSEs) of power law nonlinearity. The proposed method has some advantages. An analytical approximation can be generated in a fast converging series by applying the proposed approach. On top of that, the number of computed terms is also significantly reduced. Compared to the RDTM, the nonlinear term in this method is replaced by related Adomian polynomials prior to the implementation of a multistep approach. As a consequence, only a smaller number of NLSE computed terms are required in the attained approximation. Moreover, the approximation also converges rapidly over a

    In this paper further properties of the fuzzy complete a-fuzzy normed algebra have been introduced. Then we found the relation between the maximal ideals of fuzzy complete a-fuzzy normed algebra and the associated multiplicative linear function space. In this direction we proved that if  is character on Z then ker is a maximal ideal in Z. After this we introduce the notion structure of the a-fuzzy normed algebra then we prove that the structure, st(Z) is -fuzzy closed subset of fb(Z, ) when  (Z,  , , ) is a commutative fuzzy complete a-fuzzy normed algebra with identity e.