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This paper is devoted to the study of a fractional q-difference equation involving dual hybrid terms and equipped with nonlocal multipoint and Riemann-Liouville fractional q-integral boundary conditions. Applying a fixed point approach, we investigate the existence criteria for solutions to the given problem. Examples are constructed for illustrating the obtained results. We emphasize that our results are new in the given configuration, and some new results follow as special cases of the present ones.

In this article, we introduce and study a new class of higher-order fractional q-difference equations involving Riemann-Liouville q-derivatives with dual hybrid terms, supplemented with nonlocal multipoint q-integral boundary conditions. The existence of a unique solution to the given problem is shown by applying Banach’s fixed point theorem. We also present existing criteria for solutions to the problem at hand with the aid of Krasnoselskii’s fixed point theorem and Leray-Schauder’s nonlinear alternative. Illustrative examples are given to demonstrate the application of the obtained results.

An anomalous origin of the right coronary artery has been documented in up to 0.92% of the general population, which is more common than an anomalous origin of the left coronary artery. We present a case of an elderly hypertensive man who developed mild dyspnoea on exertion for 3 months with associated retro-sternal pain as well as occasional palpitation which all tend to subside at rest. An electrocardiogram showed evidence of left atrial enlargement. A coronary computed tomographic angiogram was acquired with a 160-slice scanner which revealed the right coronary artery to originate from the left aortic sinus with a retro-aortic pattern of anatomical course. Vascular wall calcifications were noted with multilevel luminal narrowing on the left anterior descending however distal opacification was adequate. Our case further depicts the reason for keeping in mind anatomical variations while evaluating cardiac pathologies even among Black Africans.

Introduction: Malignant causes of biliary obstruction are common in low and middle-income countries (LMICs) and patients usually present late with unresectable masses. The options for endoscopic and surgical management are scarce in many LMICs. In settings with access to ultrasound and fluoroscopy, percutaneous biliary drainage (PBD) is a promising and minimally invasive option for relieving obstruction and improving the quality of life of these patients. Method: We present a case series of six patients in northwestern Nigeria with cholestatic jaundice caused by malignant biliary obstruction successfully treated by PBD. Results: In five cases, imaging revealed a locally invasive pancreatic head mass causing obstruction. One of the patients had obstruction from biopsy-proven cholangiocarcinoma. Three patients had internal biliary drainage past the obstruction and three patients had only external biliary drainage due to the severity of the obstructions. One patient with internal drainage went on to cholangioplasty and deployment of the balloon-expandable stent over the stenotic segment. All procedures were uncomplicated and patients had a gradual clearance of jaundice and resolution of pruritus. Two of the elderly patients died within six months of the procedure (one from hepatic encephalopathy and the other from stroke). The remaining four survived but were lost to follow-up by 10 months. Conclusions: PBD is a feasible and beneficial option for decompressing malignant biliary obstruction in LMICs.

Abstract Metabolic and bariatric surgery (MBS) is widely considered the most effective option for treating obesity, a chronic, relapsing, and progressive disease. Recently, the American Society of Metabolic and Bariatric Surgery (ASMBS) and the International Federation for the Surgery of Obesity and Metabolic Disorders (IFSO) issued new guidelines on the indications for MBS, which have superseded the previous 1991 National Institutes of Health guidelines. The aim of this study is to establish the first set of consensus guidelines for selecting procedures in Class I and II obesity, using an Expert Modified Delphi Method. In this study, 78 experienced bariatric surgeons from 32 countries participated in a two-round Modified Delphi consensus voting process. The threshold for consensus was set at an agreement or disagreement of ≥ 70.0% among the experts. The experts reached a consensus on 54 statements. The committee of experts reached a consensus that MBS is a cost-effective treatment option for Class II obesity and for patients with Class I obesity who have not achieved significant weight loss through non-surgical methods. MBS was also considered suitable for patients with Type 2 diabetes mellitus (T2DM) and a body mass index (BMI) of 30 kg/m2 or higher. The committee identified intra-gastric balloon (IGB) as a treatment option for patients with class I obesity and endoscopic sleeve gastroplasty (ESG) as an option for patients with class I and II obesity, as well as for patients with T2DM and a BMI of ≥ 30 kg/m2. Sleeve gastrectomy (1) and Roux-en-Y gastric bypass (RYGB) were also recognized as viable treatment options for these patient groups. The committee also agreed that one anastomosis gastric bypass (OAGB) is a suitable option for patients with Class II obesity and T2DM, regardless of the presence or severity of obesity-related medical problems. The recommendations for selecting procedures in Class I and II obesity, developed through an Expert Modified Delphi Consensus, suggest that the use of standard primary bariatric endoscopic (IGB, ESG) and surgical procedures (SG, RYGB, OAGB) are acceptable in these patient groups, as consensus was reached regarding these procedures. However, randomized controlled trials are still needed in Class I and II Obesity to identify the best treatment approach for these patients in the future.