A numerical algorithm for solving linear and non-linear fractional differential equations is proposed based on the Bees algorithm and Chebyshev polynomials. The proposed algorithm was applied to a set of numerical examples. Faster results are obtained compared to the wavelet methods.

The aim of this paper is to investigate the theoretical approach for solvability of impulsive abstract Cauchy problem for impulsive nonlinear fractional order partial differential equations with nonlocal conditions, where the nonlinear extensible beam equation is a particular application case of this problem.

In this paper, the asymptotic behavior of all solutions of impulsive neutral differential equations with positive and negative coefficients and with impulsive integral term was investigated. Some sufficient conditions were obtained to ensure that all nonoscillatory solutions converge to zero. Illustrative examples were given for the main results.

This study presents the execution of an iterative technique suggested by Temimi and Ansari (TA) method to approximate solutions to a boundary value problem of a 4th-order nonlinear integro-differential equation (4th-ONIDE) of the type Kirchhoff which appears in the study of transverse vibration of hinged shafts. This problem is difficult to solve because there is a non-linear term under the integral sign, however, a number of authors have suggested iterative methods for solving this type of equation. The solution is obtained as a series that merges with the exact solution. Two examples are solved by TA method, the results showed that the proposed technique was effective, accurate, and reliable. Also, for greater reliability, the approxim

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.

The main aim of this paper is to apply a new technique suggested by Temimi and Ansari namely (TAM) for solving higher order Integro-Differential Equations. These equations are commonly hard to handle analytically so it is request numerical methods to get an efficient approximate solution. Series solutions of the problem under consideration are presented by means of the Iterative Method (IM). The numerical results show that the method is effective, accurate and easy to implement rapidly convergent series to the exact solution with minimum amount of computation. The MATLAB is used as a software for the calculations.           

This paper presents a numerical scheme for solving nonlinear time-fractional differential equations in the sense of Caputo. This method relies on the Laplace transform together with the modified Adomian method (LMADM), compared with the Laplace transform combined with the standard Adomian Method (LADM). Furthermore, for the comparison purpose, we applied LMADM and LADM for solving nonlinear time-fractional differential equations to identify the differences and similarities. Finally, we provided two examples regarding the nonlinear time-fractional differential equations, which showed that the convergence of the current scheme results in high accuracy and small frequency to solve this type of equations.

    This paper  concerns with the state and proof the existence and uniqueness theorem of triple state vector solution (TSVS) for the triple nonlinear parabolic partial differential equations (TNPPDEs) ,and triple state vector equations (TSVEs), under suitable assumptions. when the continuous classical triple control vector (CCTCV) is given by using the method of Galerkin (MGA). The existence theorem of a continuous classical optimal triple control vector (CCTOCV) for the continuous classical optimal control governing by the TNPPDEs under suitable conditions is proved.  

In this paper Heun method has been used to find numerical solution for first order nonlinear functional differential equation. Moreover, this method has been modified in order to treat system of nonlinear functional differential equations .two numerical examples are given for conciliated the results of this method.