In this paper we shall prepare an  sacrificial solution for fuzzy differential algebraic equations of fractional order (FFDAEs) based on the Adomian decomposition method (ADM) which is proposed to solve (FFDAEs) . The blurriness will appear in the boundary conditions, to be fuzzy numbers. The solution of the proposed pattern of  equations is studied in the form of a convergent series with readily computable components. Several examples are resolved as  clarifications, the numerical outcomes are obvious that the followed approach is simple to perform and precise when utilized to (FFDAEs).

      In this paper we shall prepare an  sacrificial solution for fuzzy differential algebraic equations of fractional order (FFDAEs) based on the Adomian decomposition method (ADM) which is proposed to solve (FFDAEs) . The blurriness will appear in the boundary conditions, to be fuzzy numbers. The solution of the proposed pattern of  equations is studied in the form of a convergent series with readily computable components. Several examples are resolved as  clarifications, the numerical outcomes are obvious that the followed approach is simple to perform and precise when utilized to (FFDAEs).

  The aim of this paper is to prove a theorem on the Riesz means of expansions with respect to Riesz bases, which extends the previous results of [1] and [2] on the Schrödinger operator and the ordinary differential operator of 4-th order to the operator of order 2m by using the eigen functions of the ordinary differential operator. Some Symbols that used in the paper:     the uniform norm. <,>   the inner product in L2. G   the set of all boundary elements of G. ˆ u   the dual function of u.

The aim of this paper is prove a theorem on the Riesz mean of expansions with respect to Riesz bases, which extends the previous results of Loi and Tahir on the Schrodinger operator to the operator of 4-th order.

The author obtain results on the asymptotic behavior of the nonoscillatory solutions of first order nonlinear neutral differential equations. Keywords. Neutral differential equations, Oscillatory and Nonoscillatory solutions.

We present a reliable algorithm for solving, homogeneous or inhomogeneous, nonlinear ordinary delay differential equations with initial conditions. The form of the solution is calculated as a series with easily computable components. Four examples are considered for the numerical illustrations of this method. The results reveal that the semi analytic iterative method (SAIM) is very effective, simple and very close to the exact solution demonstrate reliability and efficiency of this method for such problems.

This paper is dealing with non-polynomial spline functions "generalized spline" to find the approximate solution of linear Volterra integro-differential equations of the second kind and extension of this work to solve system of linear Volterra integro-differential equations. The performance of generalized spline functions are illustrated in test examples

The techniques of fractional calculus are applied successfully in many branches of science and engineering, one of the techniques is the Elzaki Adomian decomposition method (EADM), which researchers did not study with the fractional derivative of Caputo Fabrizio. This work aims to study the Elzaki Adomian decomposition method (EADM) to solve fractional differential equations with the Caputo-Fabrizio derivative. We presented the algorithm of this method with the CF operator and discussed its convergence by using the method of the Cauchy series then, the method has applied to solve Burger, heat-like, and, couped Burger equations with the Caputo -Fabrizio operator. To conclude the method was convergent and effective for solving this type of

      In this paper, several types of space-time fractional partial differential equations has been solved by using most of special double linear integral transform ”double  Sumudu ”. Also, we are going to argue the truth of these solutions by another analytically method “invariant subspace method”. All results are illustrative numerically and graphically.