This work discusses the beginning of fractional calculus and how the Sumudu and Elzaki transforms are applied to fractional derivatives. This approach combines a double Sumudu-Elzaki transform strategy to discover analytic solutions to space-time fractional partial differential equations in Mittag-Leffler functions subject to initial and boundary conditions. Where this method gets closer and closer to the correct answer, and the technique's efficacy is demonstrated using numerical examples performed with Matlab R2015a.

Background: Differentiation between malignant and benign vertebral compression fracture is often problematic. This is precisely difficult in elderly who are predisposed to benign compression caused by osteoporosis .Establishing correct diagnosis is of great importance in determining the treatment andprognosis.A study was performed to determine which magnetic resonance imaging findings are useful in discrimination between metastatic and acute osteoporotic compression fractures of the spine. Recently MRI is being increasingly used for evaluation of these fractures.Objectives: The aim of this study is to establish the correct diagnosis of malignant and benign compression vertebral fracture by MRI to determine treatment and prognosis.Methods

<p>Daftardar Gejji and Hossein Jafari have proposed a new iterative method for solving many of the linear and nonlinear equations namely (DJM). This method proved already the effectiveness in solved many of the ordinary differential equations, partial differential equations and integral equations. The main aim from this paper is to propose the Daftardar-Jafari method (DJM) to solve the Duffing equations and to find the exact solution and numerical solutions. The proposed (DJM) is very effective and reliable, and the solution is obtained in the series form with easily computed components. The software used for the calculations in this study was MATHEMATICA^® 9.0.</p>

Deep drawing process to produce square cup is very complex process due to a lot of process parameters which control on this process, therefore associated with it many of defects such as earing, wrinkling and fracture. Study of the effect of some process parameters to determine the values of these parameters which give the best result, the distributions for the thickness and depths of the cup were used to estimate the effect of the parameters on the cup numerically, in addition to experimental verification just to the conditions which give the best numerical predictions in order to reduce the time, efforts and costs for producing square cup with less defects experimentally is the aim of this study. The numerical analysis is used to study

The m-consecutive-k-out-of-n: F linear and circular system consists of n sequentially connected components; the components are ordered on a line or a circle; it fails if there are at least m non-overlapping runs of consecutive-k failed components. This paper proposes the reliability and failure probability functions for both linearly and circularly m-consecutive-k-out-of-n: F systems. More precisely, the failure states of the system components are separated into two collections (the working and the failure collections); where each one is defined as a collection of finite mutual disjoint classes of the system states. Illustrative example is provided.

Objective: to assess the predictive value of Doppler imaging of the uterine artery in the identification of early intrauterine abnormal pregnancy as compared to a normal intrauterine pregnancy. Subjects and methods: one hundred and twenty pregnant ladies, at their 6-12 weeks of gestation, with a singleton pregnancy were included in this population-based case-control study. Thirty women with a missed miscarriage, 30 with hydatidiform mole, 30 with a blighted ovum, and 30 as a control group, without risk factors, underwent Doppler interrogation of the uterine arteries. Resistive index (RI), pulsatility index (PI), and the systolic/diastolic ratio (S/D) were measured for both sides. The t-test, or ANOVA test when appropriate, was

Objective: to assess the predictive value of Doppler imaging of the uterine artery in the identification of early intrauterine abnormal pregnancy as compared to a normal intrauterine pregnancy.

Subjects and methods: one hundred and twenty pregnant ladies, at their 6-12 weeks of gestation, with a singleton pregnancy were included in this population-based case-control study. Thirty women with a missed miscarriage, 30 with hydatidiform mole, 30 with a blighted ovum, and 30 as a control group, without risk factors, underwent Doppler interrogation of the uterine arteries. Resistive index (RI), pulsatility index (PI), and the systolic/diastolic ratio (S/D) were measured for both sides. The t-test, or ANOVA test when a

Background: Prolapsed intervertebral disc is an important and common cause of low backache. MRI has now become universally accepted investigation for prolapsed intervertebral disc. We, however, regularly come across situations, when MRI shows diffuse disc bulges, even at multiple levels, which cannot be correlated clinically and when such cases are operated, no significant disc prolapse is found resulting in negative exploration. Objective: To evaluate the role of M.R.I. finding not only for diagnosis of disc herniation at lumbar region but also for localization the level of herniation Methods: A prospective study on seventy five symptomatic low backache and MRI confirmed prolapsed intervertebral disc patients at lumbo-sacral region were op

Background: Prolapsed intervertebral disc is an important and common cause of low backache. MRI has now become universally accepted investigation for prolapsed intervertebral disc. We, however, regularly come across situations, when MRI shows diffuse disc bulges, even at multiple levels, which cannot be correlated clinically and when such cases are operated, no significant disc prolapse is found resulting in negative exploration.Objective: To evaluate the role of M.R.I. finding not only for diagnosis of disc herniation at lumbar region but also for localization the level of herniationMethods: A prospective study on seventy five symptomatic low backache and MRI confirmed prolapsed intervertebral disc patients at lumbo-sacral region were o