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.

Background: Ambulatory peritoneal dialysis
introduced by Popvich et al (13) in 1978 , consists of a
four to five hours lavage of peritoneal cavity with 2000
ml of glucose solution .It remains a useful method for
treating patients with end stage renal failure till renal
transplantation becomes possible.
Objectives: The aim of the study is to evaluate the
value of cytological changes of mesothelial cells in
dialysate patients.
Methods: Within one year period, 32 cytological
peritoneal fluid samples were collected from patients
with end stage renal failure regardless of the underlying
causes, admitted to the dialyzing unit in Kadimya
Teaching Hospital. Smears were prepared and fixed in
95 % ethyl al

Seventy exudative lymphocytic pleural fluid specimens of patients with suspected tuberculous pleural effusion submitted to the National Reference Laboratory of tuberculosis/Baghdad from October 2012 to February 2013. These effusions were due to tuberculosis pleuritis (n=12) and non-tuberculosis pleuritis (n=58). The following parameters were analyzed: protein concentration, glucose concentration, lactate dehydrogenase (LDH) concentration and adenosine deaminase activity (ADA). As a result, the protein concentration was higher in TPE patients (8.80 ± 0.89 g/dl) than it's concentration in non-TPE patients (7.61 ± 0.54 g/dl), as well as LDH concentration was (3366.58 ± 284.28 U/L) in TPE patients and (3024.12 ± 116.84 U/L) in non-TPE pa

      This paper intends to initiate a new type of generalized closed set in topological space with the theoretical application of generalized topological space. This newly defined set is a weaker form than the -closed set as well as -closed set. Some phenomenal characterizations and results of newly defined sets are inculcated in a proper manner. The characteristics of normal spaces and regular spaces are achieved in the light of the generalized pre-regular closed set.

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.

     The goal of this study is to investigate the effects of heat transfer on a non-uniform inclined asymmetrical channel with couple stress fluids via a porous medium using incline magnetohydrodynamics. The governing equation is studied while using low Reynolds approximations and long-wavelength assumptions. Mathematical expressions for (pressure gradient), (temperature), (axial velocity), (heat temperature coefficient), and (stream function). A precise set of values for the various parameters in the present model has been used. The mathematical expressions for axial velocity, stream function, pressure gradient, and pressure rise per wavelength have been derived analytically. "MATHEMATICA" is used to present the computational result

A modified Leslie-Gower predator-prey model with a Beddington-DeAngelis functional response is proposed and studied. The purpose is to examine the effects of fear and quadratic fixed effort harvesting on the system's dynamic behavior. The model's qualitative properties, such as local equilibria stability, permanence, and global stability, are examined. The analysis of local bifurcation has been studied. It is discovered that the system experiences a saddle-node bifurcation at the survival equilibrium point whereas a transcritical bifurcation occurs at the boundary equilibrium point. Additionally established are the prerequisites for Hopf bifurcation existence. Finally, using MATLAB, a numerical investigation is conducted to verify t