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Anew class of implicit Hadamard fractional differential equations with Riemann-Stieltjes integral boundary conditions is studied in this research paper. The existence and uniqueness results of the aforesaid problem are investigated using Schauder’s fixed point theorem and Banach’s contraction mapping principle. A simulative example is given to highlight the acquired outcomes.

In the current manuscript, we combine the q-fractional integral operator and q-fractional derivative to investigate a coupled hybrid fractional q-differential systems with sequential fractional q-derivatives. The existence and uniqueness of solutions for the proposed system are established by means of Leray-Schauder’s alternative and the Banach contraction principle. Furthermore, the Ulam-Hyers and Ulam-Hyers-Rassias stability results are discussed. Finally, two illustrative examples are given to highlight the theoretical findings.

In this paper, we consider a new coupled system of fractional boundary value problems based on the thermostat control model. With the help of fixed point theory, we investigate the existence criterion of the solution to the given coupled system. This property is proved by using the Krasnoselskii’s fixed point theorem and its uniqueness is proved via the Banach principle for contractions. Further, the Hyers–Ulam stability of solutions is investigated. Then, we find the approximate solution of the coupled fractional thermostat control system by using a numerical technique called the generalized differential transform method. To show the consistency and validity of our theoretical results, we provide two illustrative examples.

Background Gliomas are characterized by high morbidity and mortality with low cure and high recurrence rates, which depends to a great degree on the angiogenesis of the tumor. Assessment of such angiogenesis by perfusion techniques is of utmost importance for the preoperative grading of gliomas. The purpose of this study was to assess the role of arterial spin labeling (ASL) perfusion as a non-contrast MRI technique in the grading of brain gliomas, in correlation with the dynamic susceptibility contrast perfusion imaging (DSC-PI). The study was carried out on 35 patients admitted to the Neurosurgery Department with MRI features of gliomas and sent for further perfusion imaging. Non-contrast ASL followed by DSC-PI was done for all cases. The final diagnosis of the cases was established by histopathology. Results Fourteen patients (14/35) had low-grade gliomas while twenty-one (21/35) had high-grade gliomas. In low-grade gliomas, four cases out of 14 were falsely graded as high-grade tumors showing hyperperfusion on ASL, three of which showed DSC-PI hypoperfusion. In high-grade gliomas, two cases out of 21 were interpreted as an indeterminate grade by ASL showing isoperfusion, however showed hyperperfusion on DSC-PI. ROC curve analysis showed ASL-derived rCBF > 2.08 to have 80.95% sensitivity, 85.71% specificity, and overall accuracy of 82.86% compared to 100% sensitivity, specificity, and accuracy of DSC-PI-derived rCBV and rCBF of > 1.1 and > 0.9, respectively. A significant positive correlation was noted between ASL and DSC-PI with correlation coefficient reaching r = 0.80 between ASL-rCBF and DSC-rCBF (p < 0.01) and r = 0.68 between ASL and DSC-rCBV (p < 0.01). Conclusions ASL is a relatively recent non-contrast perfusion technique that obtains results which are in fair agreement with the more established DSC perfusion imaging making it an alternative method for preoperative assessment of perfusion of gliomas, especially for patients with contraindications to contrast agents.

In this paper, we study the existence and uniqueness of solutions for Riemann–Stieltjes integral boundary value problems of nonlinear implicit Hadamard fractional differential equations. The investigation of the main results depends on Schauder’s fixed point theorem and Banach’s contraction principle. An illustrative example is given to show the applicability of theoretical results.

The object of investigation in this paper is a scalar linear fractional differential equation with generalized proportional derivative of Riemann–Liouville type (LFDEGD). The main goal is the obtaining an explicit solution of the initial value problem of the studied equation. Note that the locally solvability, being the same as the existence of solutions to the initial value problem, is connected with the symmetry of a transformation of a system of differential equations. At the same time, several criteria for existence of the initial value problem for nonlinear fractional differential equations with generalized proportional derivative are connected with the linear ones. It leads to the necessity of obtaining an explicit solution of LFDEGD. In this paper two cases are studied: the case of no impulses in the differential equation are presented and the case when instantaneous impulses at initially given points are involved. All obtained formulas are based on the application of Mittag–Leffler function with two parameters. In the case of impulses, initially the appropriate impulsive conditions are set up and later the explicit solutions are obtained.

A newly proposed p-Laplacian nonperiodic boundary value problem is studied in this research paper in the form of generalized Caputo fractional derivatives. The existence and uniqueness of solutions are fully investigated for this problem using some fixed point theorems such as Banach and Schauder. This work is supported with an example to apply all obtained new results and validate their applicability.

In this paper we discuss the solvability of Langevin equations with two Hadamard fractional derivatives. The method of this discussion is to study the solutions of the equivalent Volterra integral ...

Background Data: Discectomy through a limited laminotomy has remained the “gold standard” for lumbar disc surgery. Surgery for lumbar disc herniation can be classified into two broad categories;open (conventional) versus minimally invasive surgery, where the last category classified into microscopic, endoscopic and percutaneous procedures. Microendoscopic discectomy (MED) is unique in that it combines open surgical principles with endoscopic technology. Purpose: To evaluate extent of tissue damage and pain relief after microendoscopic (MED) and microscopic lumbar discectomy (MD). Study Design: A prospective randomized controlled study. Patients and Methods: The study included 40 patients having lumbar disc prolapse, operated in Alexandria Main University Hospital. Twenty of them underwent MED (Group A) and the other twenty underwent MD (Group B). Clinical (VAS, ODI) and radiological and biochemical markers (CRP, CPK) for tissue inflammation data were collected preoperatively and postoperatively for comparison. Patients were followed up for 6 months. Results: 26 patients were males and 14 were females. The mean age for group A was 40.8±1.34 years and for group B was 40.2±1.06 years. Clinically all patients had low back pain and radicular leg pain. There was no statistically significant difference between the duration of surgery in both groups. The length of hospital stay was significantly less in MED group. The length of the skin wound was significantly less in MED group. Reduction of back pain VAS immediate and 1 month postoperative was reported in both groups and was statistically significantly better in MED group, however, after 6 months there was no difference between both groups. There was significant improvement with no difference between both groups regarding radicular VAS and ODI all through the follow up. Postoperative CRP and CPK was statistically significantly higher in MD group (P

This paper is concerned with the existence and uniqueness of solutions for Hadamard and Riemann–Liouville fractional neutral functional integrodifferential equations with finite delay. The existence of solutions is derived from Leray–Schauders alternative, whereas the uniqueness of solution is established by Banachs contraction principle. An illustrative example is also included.

Background Data: Lumbar spinal stenosis refers to the anatomical narrowing of the lumbar spinal canal, and is associated with a spectrum of clinical symptoms. The annual incidence of lumbar spinal stenosis is reported to be five cases per 100,000 individuals. Purpose: The purpose of this study is to evaluate the surgical outcome of patients having lumbar spinal stenosis and underwent unilateral approach for bilateral spinal decompression surgery, and to compare outcomes with the conventional laminectomy approach. Study Design: This is a prospective randomized controlled study. Patients and Methods: This study included 21 patients with clinically manifest disco-ligamentous lumbar spinal stenosis without radiological instability. Eleven patients had bilateral neural decompression through a unilateral microscopic approach (unilateral laminectomy) (Group-I) and the other 10 patients had conventional laminectomy (Group-II).Clinical assessment was done using Visual Analogue Scale (VAS) and ODI. The patients were followed-up for 12 months postoperatively. Results: Thirteen patients were females and 8 were males. The mean age of unilateral approach group was 47.2 years, and 49.5 years for the conventional group. Reported duration of surgery was 100 minutes in group-I and 85 minutes group-II. Reported intraoperative blood loss was 84.7 cc in group-I, and 127 cc in group-II. Clinical improvement was achieved in both groups without significant difference in between regarding VAS and ODI. In group we reported unintended durotomy occurred in two patients, CSF leak in one patient, and hematoma in another patient. In group-I we had one patient of unintended durotomy, one patient had CSF leak, and one patient developed spondylolisthesis. Conclusion: Unilateral microscopic laminoforaminotomy with cross over the top technique, for bilateral neural decompression in lumbar spinal stenosis has equal efficacy and safety with minimal effect on stability and slight better postoperative back pain in comparison to conventional approach. (2017ESJ140)

This paper is devoted to initial value problems for impulsive fractional differential equations of Caputo–Fabrizio type fractional derivative. By means of Banach’s fixed point theorem and Schaefer’s fixed point theorem, the existence and uniqueness results are obtained. Finally, an example is given to illustrate one of the main results.

In this paper we study the existence and uniqueness of a solution for fractional impulsive differential equations with Riemann-Liouville integral boundary condition, using a fixed point theorem. Also, we discuss Ulamstability for these equations via some generalized singular Gronwall inequalities.

This paper concerns the existence of mild solutions for some fractional Cauchy problem with nonlocal conditions in the α-norm. The linear part of the equations is assumed to generate an analytic compact bounded semigroup, and the nonlinear part satisfies some Lipschitz conditions with respect to the fractional power norm of the linear part. By using a fixed point theorem of Sadovskii, we establish some existence results which generalize ones in the case of fractional order derivative.

Background and Objectives The present study is focused on correlation of parent vessels and neck diameters with anterior communicating artery (AComA) aneurysmal depth and growth direction. The study principally aims to suggest a new classification of AComA-located aneurysms based on the physical characteristics of parent vessels. Methods A retrospective analysis was performed of 155 patients with ruptured AComA-located aneurysms. The percentage of difference between both A1 arteries was measured on computed tomography angiography images and neck locations were determined. Accordingly, AComA-located aneurysms were classified into 2 groups. In both groups, A1 and A2 arteries and neck size diameters were measured and their relation with aneurysmal depth was studied. The aspect ratio was calculated. Results Eleven patients in which the aneurysm neck originates from the AComA proper with almost equal A1s were classified as the true AComA aneurysm group whereas 144 patients in whom the aneurysm neck originates at the dominant A1 bifurcation into the AComA and A2 with the average difference between both A1s of about 84.44% were classified as the dominant A1-bifurcation group. There is significant correlation between aneurysmal depth and neck diameter in both groups ( P ≤ 0.05, P Conclusions The dominant A1 bifurcation type is the most common type of AComA-located aneurysm. The present classification provides clinical value in understanding how AComA aneurysms grow and behave. It helps to understand the geometry of multilobulated aneurysms such as ruptured blebs locations during treatment procedures respecting the direction of the dominant A1 axis in group II. Multiple anatomic variations of this complex AComA area can clarify future subtypes of these 2 groups. Thus, further investigation of more patients is needed.

We study nonlinear singular integral equation of Volterra type in Banach space of real functions defined and continuous on a bounded and closed interval. Using a suitable measure of noncompactness we prove the existence of monotonic solutions. Also a generalized result is taken in the consideration. Mathematics Subject Classification: 32A55, 11D09

Penetrating head injuries with impacted foreign bodies are rare, associated with a high incidence of morbidity and potentially life-threatening. In this study, we aimed at investigating the outcome of these cases as well as analyzing the factors affecting the prognosis. A retrospective study in which the records of 16 patients who had penetrating head injuries caused by low-velocity impacted foreign bodies were revised. All patients were males with a mean age of 28.9 years (range, 18 to 50 years). The follow-up period ranged from 4 to 13 months with a mean of 8.1 months. Causes of injury were construction accidents in 6 (37.5 %) patients, assault in 6 (37.5 %) and road traffic accidents in 4 (25 %). The impacted objects included a bar of iron, a piece of wood, a nail, a sickle and a piece of glass. Diagnostic computerized tomography (CT) of the brain was carried out on admission in all patients. Thirteen (81.3 %) patients were submitted to surgery, and all had the appropriate management in the form of antibiotics and dehydrating measures as required. The primary outcome measure was the Glasgow Outcome Scale (GOS) at the end of follow-up. At the end of follow-up, ten (62.5 %) patients had a GOS score of 5, two (12.5 %) patients had a score of 4, and four (25 %) patients had a score of 1. Low-velocity penetrating head injuries are most common in young adult males. With the appropriate management, a majority of even the most severe cases can have a favorable outcome.

In this paper, for the first time, we introduce and study the new concepts near closure operators induced from binary relation. These operators represent a generalization to closure operators that are induced from binary relations. The suggested techniques will narrow the gap between topologists and those who are interested in applications with topology in their field. The fundamental properties of the suggested structures are obtained. Finally, we introduce some applications of the suggested structures in rough set theory. Moreover, we give a simple practical example to illustrate the importance of near concepts in rough set theory and we introduce comparisons between our approaches and other approaches.