Some nonlinear differential equations with fractional order are evaluated using a novel approach, the Sumudu and Adomian Decomposition Technique (STADM). To get the results of the given model, the Sumudu transformation and iterative technique are employed. The suggested method has an advantage over alternative strategies in that it does not require additional resources or calculations. This approach works well, is easy to use, and yields good results. Besides, the solution graphs are plotted using MATLAB software. Also, the true solution of the fractional Newell-Whitehead equation is shown together with the approximate solutions of STADM. The results showed our approach is a great, reliable, and easy method to deal with specific problems

In this paper, the continuous classical boundary optimal control problem (CCBOCP) for triple linear partial differential equations of parabolic type (TLPDEPAR) with initial and boundary conditions (ICs & BCs) is studied. The Galerkin method (GM) is used to prove the existence and uniqueness theorem of the state vector solution (SVS) for given continuous classical boundary control vector (CCBCV). The proof of the existence theorem of a continuous classical boundary optimal control vector (CCBOCV) associated with the TLPDEPAR is proved. The derivation of the Fréchet derivative (FrD) for the cost function (CoF) is obtained. At the end, the theorem of the necessary conditions for optimality (NCsThOP) of this problem is stated and prov

           In this paper, the homotopy perturbation method (HPM) is presented for treating a linear system of second-kind mixed Volterra-Fredholm integral equations. The method is based on constructing the series whose summation is the solution of the considered system. Convergence of constructed series is discussed and its proof is given; also, the error estimation is obtained. Algorithm is suggested and applied on several examples and the results are computed by using MATLAB (R2015a). To show the accuracy of the results and the effectiveness of the method, the approximate solutions of some examples are compared with the exact solution by computing the absolute errors.

While analytical solutions to Quadratic Assignment Problems (QAP) have indeed been since a long time, the expanding use of Evolutionary Algorithms (EAs) for similar issues gives a framework for dealing with QAP with an extraordinarily broad scope. The study's key contribution is that it normalizes all of the criteria into a single scale, regardless of their measurement systems or the requirements of minimum or maximum, relieving the researchers of the exhaustively quantifying the quality criteria. A tabu search algorithm for quadratic assignment problems (TSQAP) is proposed, which combines the limitations of tabu search with a discrete assignment problem. The effectiveness of the proposed technique has been compared to well-established a

Some nonlinear differential equations with fractional order are evaluated using a novel approach, the Sumudu and Adomian Decomposition Technique (STADM). To get the results of the given model, the Sumudu transformation and iterative technique are employed. The suggested method has an advantage over alternative strategies in that it does not require additional resources or calculations. This approach works well, is easy to use, and yields good results. Besides, the solution graphs are plotted using MATLAB software. Also, the true solution of the fractional Newell-Whitehead equation is shown together with the approximate solutions of STADM. The results showed our approach is a great, reliable, and easy method to deal with specific problems in

In this paper, the linear system of Fredholm integral equations is solving using Open Newton-Cotes formula, which we use five different types of Open Newton-Cotes formula to solve this system.  Compare the results of suggested method with the results of another method (closed Newton-Cotes formula)    Finally, at the end of each method, algorithms and programs developed and written in MATLAB (version 7.0) and we give some numerical examples, illustrate suggested method

In this paper, the proposed phase fitted and amplification fitted of the Runge-Kutta-Fehlberg method were derived on the basis of existing method of 4(5) order to solve ordinary differential equations with oscillatory solutions. The recent method has null phase-lag and zero dissipation properties. The phase-lag or dispersion error is the angle between the real solution and the approximate solution. While the dissipation is the distance of the numerical solution from the basic periodic solution. Many of problems are tested over a long interval, and the numerical results have shown that the present method is more precise than the 4(5) Runge-Kutta-Fehlberg method.

     The aim of this paper is to study the nonlinear delay second order eigenvalue problems which consists of delay ordinary differential equations, in fact one of the expansion methods that is called the least square method which will be developed to solve this kind of problems.

The fractional order partial differential equations (FPDEs) are generalizations of classical partial differential equations (PDEs). In this paper we examine the stability of the explicit and implicit finite difference methods to solve the initial-boundary value problem of the hyperbolic for one-sided and two sided fractional order partial differential equations (FPDEs). The stability (and convergence) result of this problem is discussed by using the Fourier series method (Von Neumanns Method).

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  This study is concerned with the estimation of constant  and time-varying parameters in non-linear ordinary differential equations, which do not have analytical solutions. The estimation is done in a multi-stage method where constant and time-varying parameters are estimated in a straight sequential way from several stages. In the first stage, the model of the differential equations is converted to a regression model that includes the state variables with their derivatives and then the estimation of the state variables and their derivatives in a penalized splines method and compensating the estimations in the regression model. In the second stage, the pseudo- least squares method was used to es