In this paper, we present an approximate analytical and numerical solutions for the differential equations with multiple delay using the extend differential transform method (DTM). This method is used to solve many linear and non linear problems.

In this paper, a sufficient condition for stability of a system of nonlinear multi-fractional order differential equations on a finite time interval with an illustrative example, has been presented to demonstrate our result. Also, an idea to extend our result on such system on an infinite time interval is suggested.

In this work, we employ a new normalization Bernstein basis for solving linear Freadholm of fractional integro-differential equations  nonhomogeneous  of the second type (LFFIDE_s). We adopt Petrov-Galerkian method (PGM) to approximate solution of the (LFFIDE_s) via normalization Bernstein basis that yields linear system. Some examples are given and their results are shown in tables and figures, the Petrov-Galerkian method (PGM) is very effective and convenient and overcome the difficulty of traditional methods. We solve this problem (LFFIDE_s) by the assistance of Matlab10.   

Due to its importance in physics and applied mathematics, the non-linear Sturm-Liouville problems
witnessed massive attention since 1960. A powerful Mathematical technique called the Newton-Kantorovich
method is applied in this work to one of the non-linear Sturm-Liouville problems. To the best of the authors’
knowledge, this technique of Newton-Kantorovich has never been applied before to solve the non-linear
Sturm-Liouville problems under consideration. Accordingly, the purpose of this work is to show that this
important specific kind of non-linear Sturm-Liouville differential equations problems can be solved by
applying the well-known Newton-Kantorovich method. Also, to show the efficiency of appl

This paper is concerned with combining two different transforms to present a new joint transform FHET and its inverse transform IFHET. Also, the most important property of FHET was concluded and proved, which is called the finite Hankel – Elzaki transforms of the Bessel differential operator property, this property was discussed for two different boundary conditions, Dirichlet and Robin. Where the importance of this property is shown by solving axisymmetric partial differential equations and transitioning to an algebraic equation directly. Also, the joint Finite Hankel-Elzaki transform method was applied in solving a mathematical-physical problem, which is the Hotdog Problem. A steady state which does not depend on time was discussed f

This paper presents a new transform method to solve partial differential equations, for finding suitable accurate solutions in a wider domain. It can be used to solve the problems without resorting to the frequency domain. The new transform is combined with the homotopy perturbation method in order to solve three dimensional second order partial differential equations with initial condition, and the convergence of the solution to the exact form is proved. The implementation of the suggested method demonstrates the usefulness in finding exact solutions. The practical implications show the effectiveness of approach and it is easily implemented in finding exact solutions.

       Finally, all algori

This research discussed, the process of comparison between the regression model of partial least squares and tree regression, where these models included two types of statistical methods represented by the first type "parameter statistics" of the partial least squares, which is adopted when the number of variables is greater than the number of observations and also when the number of observations larger than the number of variables, the second type is the "nonparametric statistic" represented by tree regression, which is the division of data in a hierarchical way. The regression models for the two models were estimated, and then the comparison between them, where the comparison between these methods was according to a Mean Square