Abstract: In this paper, a nonlinear fractional diffusion and wave equations are solved using the Abaoub-Shkheam Decomposition Method (QDM). The Caputo sense is used to characterise the fractional derivative. An example is provided to demonstrate the method's efficiency and practicality.

Abstract: The Abaoub-Shkheam Decomposition Method (QDM) is employed in this paper to solve nonlinear initial value problems of second order. Adomian polynomial is used to decompose nonlinear functions that exist in a given equation. We are using this method (QDM) to find the exact solution of different types of non-linear ordinary differential equations, which is based on the Abaoub Shkheam transform method (QTM) and the Adomian Decomposition Method (ADM). An example is provided to demonstrate the efficacy of this approach. 

In the current study a new family of distributions called the odd Lindley Log compound Rayleigh distribution is introduced and studied. Some statistical properties of the new distribution including moments, moment generating function and Renyi entropy are derived. Parameter estimations are obtained via the maximum likelihood method and the observed information matrix is derived. Finally, a real dataset is used to illustrate the importance and flexibility of the new proposed distribution.

Keywords—Odd Lindley, Rayleigh, Distribution, Entropy

Abstract: In this study, we introduce a novel approach to the solution of a nonlinear Volterra -Fredholm integral equations by applying the Adomian decomposition method under the effect of the Abaoub- Shkheam transform. We demonstrate the existence and uniqueness of the solution in Banach space and illustrate this idea with an example.

In this work,we investigate Frobenius companion matrices with entries from the ring of integers modulo a prime number. We introduce a mapping 𝝍to construct a directed graph, where vertices represent these matrices and edges are defined by 𝝍. Our analysis focuses on the structure and properties of this directed graph, including vertex degrees, cycles, and connected components, in relation to theeigenvalues of the matrices

In this work, we investigate essential definitions, defining 𝐺 as a simple graph with vertices in ℤ𝑛 and subgraphs Γ𝑢 and Γ𝑞 as unit residue and quadratic residue graphs modulo 𝑛, respectively. The investigation extends to the degree of 𝐺, Γ𝑢, and Γ𝑞, illuminating the properties of these subgraphs in the context of quadratic congruences.

The current research investigates the use of logistic regression as a statistical technique for modelling real blood pressure (BP) data. This study uses a dataset collected from a desert community in southwestern Libya. Six factors that are widely believed to play an important role in the process of BP were considered. Statistical analyses of the available dataset revealed that the main cause of hypertension in such community is age. The proposed multiple logistic regression analysis also revealed that two factors, age and systolic BP, showed greater significance among the six examined variables. These two variables were identified as having a significant effect on blood pressure performance. Based on a determined criterion, each page as the main cause of hypertension in such community participants was classified as hypertensive or not, significant variables were selected based on the p-value associated with the model significance level, and these factors were selected based on the criteria to achieve the model significance level (p < 0.05). The statistical analysis was carried out using R language.

 عن الدوال التوافقية، لذلك قدمنا أوال أهه النظزيات املتعلقة بالدوال التوافقية،

وطزح فكزة املزافق التوافقي. وقدمنا أيضا مفووو جزين ومسألة ديزيشليى. وخلصنا إىل أن الدوال التوافقية

هلا العديد من التطبيقات ميكن استدداموا يف دراسة القزص وفوه مسألة ديزيشليى.

In this paper, we apply the auxiliary equation method with the aid of symbolic

computer algebra system (CAS) such as Maple or Mathematica to construct

many new exact traveling wave solutions of a singularly perturbed generalized

Gardner equation with nonlinear terms of any order. Using a simple

transformation, this equation can be reduced to a nonlinear ordinary differential

equation (ODE). A comparison between our results and the well-known results

is given. Further, plotting 2D and 3D graphics of the exact solutions are shown.

In the present article, we are going to highlight the relation between different digraphs (cycles) of finite commutative ring Zn for a natural number n, under the map (a,b) → (a+b,ab). The algorithm, which is used to perform the calculations, has been built in MATLAB®.