In this paper, cubic trigonometric spline is used to solve nonlinear Volterra integral equations of second kind. Examples are illustrated to show the presented method’s efficiency and convenience.

In this study, He's parallel numerical algorithm by neural network is applied to type of integration of fractional equations is Abel’s integral equations of the 1^st and 2^nd kinds. Using a Levenberge – Marquaradt training algorithm as a tool to train the network. To show the efficiency of the method, some type of Abel’s integral equations is solved as numerical examples. Numerical results show that the new method is very efficient problems with high accuracy.

In this paper, we will study and prove the existence and the uniqueness theorems
of solutions of the generalized linear integro-differential equations with unequal
fractional order of differentiation and integration by using Schauder fixed point
theorem. This type of fractional integro-differential equation may be considered as a
generalization to the other types of fractional integro-differential equations
Considered by other researchers, as well as, to the usual integro-differential
equations.

In this paper, we consider inequalities in which the function is an element of n-th partially order space. Local and Global uniqueness theorem of solutions of the n-the order Partial differential equation Obtained which are applications of Gronwall's inequalities.

An efficient combination of Adomian Decomposition iterative technique coupled with Laplace transformation to solve non-linear Random Integro differential equation (NRIDE) is introduced in a novel way to get an accurate analytical solution. This technique is an elegant combination of theLaplace transform, and the Adomian polynomial. The suggested method will convert differential equations into iterative algebraic equations, thus reducing processing and analytical work. The technique solves the problem of calculating the Adomian polynomials. The method’s efficiency was investigated using some numerical instances, and the findings demonstrate that it is easier to use than many other numerical procedures. It has also been established that (LT

BACKGROUND: Breast cancer remains the most common malignancy among the Iraqi population. Affected patients exhibit different clinical behaviours according to the molecular subtypes of the tumour. AIM: To identify the clinical and pathological presentations of the Iraqi breast cancer subtypes identified by Estrogen receptors (ER), Progesterone receptors (PR) and HER2 expressions. PATIENTS AND METHODS: The present study comprised 486 Iraqi female patients diagnosed with breast cancer. ER, PR and HER2 contents of the primary tumours were assessed through immunohistochemical staining; classifying the patients into five different groups: Triple Negative (ER/PR negative/HER2 negative), Triple Positive (ER/PR positive/HER2 positive), Luminal A (ER

The nuclear structure for the positive ( ) States and negative ( ) states of ^36,40Ar nuclei have been studied via electromagnetic transitions within the framework of shell model. The shell model analysis has been performed for the electromagnetic properties, in particular, the excitation energies, occupancies numbers, the transition strengths B(CL) and the elastic and inelastic electron scattering longitudinal form factors. Different model spaces with different appropriate interactions have been considered for all selected states. The deduced results for the (CL) longitudinal form factors and other properties have been discussed and compared with the available experimental data. The inclusion of the effective

In this paper, the series solution is applied to solve third order fuzzy differential equations with a fuzzy initial value. The proposed method applies Taylor expansion in solving the system and the approximate solution of the problem which is calculated in the form of a rapid convergent series; some definitions and theorems are reviewed as a basis in solving fuzzy differential equations. An example is applied to illustrate the proposed technical accuracy. Also, a comparison between the obtained results is made, in addition to the application of the crisp solution, when the-level equals one.

Recently, the financial mathematics has been emerged to interpret and predict the underlying mechanism that generates an incident of concern. A system of differential equations can reveal a dynamical development of financial mechanism across time. Multivariate wiener process represents the stochastic term in a system of stochastic differential equations (SDE). The standard wiener process follows a Markov chain, and hence it is a martingale (kind of Markov chain), which is a good integrator. Though, the fractional Wiener process does not follow a Markov chain, hence it is not a good integrator. This problem will produce an Arbitrage (non-equilibrium in the market) in the predicted series. It is undesired property that leads to erroneous conc

In This paper generalized spline method and Caputo differential operator is applied to solve linear fractional integro-differential equations of the second kind. Comparison of the applied method with exact solutions reveals that the method is tremendously effective.