This current work is devoted to develop qualitative theory of existence of solution to some families of fractional order differential equations (FODEs). For this purposes we utilize fixed point theory due to Banach and Schauder. Further using differential transform method (DTM), we also compute analytical or semi-analytical results to the proposed problems. Also by some proper examples we demonstrate the results.

Background: Laparoscopic Left hepatectomy is gaining acceptance in the surgical community as a viable option for patients with hepatic malignancies. We present a case of Laparoscopic Left hepatectomy for an intra-hepatic cholangiocarcinoma patient performed using the Machado's extra-glissonian inflow pedicle technique. Methods: Video presentation of a laparoscopic Left hepatectomy. Results: Operative time was 6 hours. No post operative complications were encountered. Blood loss was 120 mLs. Patient was discharged on day 3. Histopathology showed an intra-hepatic cholangiocarcinoma with R0 margin. She is alive and well 2 years postoperative with no evidence of recurrence. Conclusions: Laparoscopic Left Hepatectomy using Machado extra-glissonian technique is a feasible option for patients with intra-hepatic cholangio-carcinoma.

Background: Laparoscopic Pancreatico-duodenectomy is a technically challenging procedure that is slowly finding its way in routine clinical practice. We started on our Laparoscopic journey in April 2021 and have subsequently performed over 10 totally laparoscopic pancreatico-duodenectomies. We present a video presentation of our first laparoscopic Pancreatico-duodenectomy performed in khyber pakhtunkhwa province of Pakistan. Methods: Video presentation of Pancreatico-duodenectomy with modified blumgart technique. Results: Operative time was 7 hours. Blood loss was 230 mLs. There was no post operative complications including no clinically relevant pancreatic leak. Length of stay was 5 days. Post op histopathology showed Grade 2 neuroendocrine tumour with R0 margin. Conclusions: Laparoscopic Pancreatico-duodenectomy is feasible in a resource limited setting and may have a role in better patient recovery.

Background:The first Hepato-Pancreatico-Biliary (HPB) center was established in 2021 at Shaukat Khanum Memorial Hospital and Research hospital (SKM&RH), Peshawar in the Khyber Pakhtunkhwa province of Pakistan. Being a resource poor province with minimal exposure to complex HPB surgery brought it sown challenges including trained workforce, lack of equipment and financial constraints. We compare our 1 year outcome and discuss the challenges faced in setting up a new HPB unit where non-existed before. Methods: We retrospectively analyzed our prospectively maintained database for all liver resections performed by a single liver surgeon to determine the short-term outcomes at our newly established HBP center. The Intra-operative variables studied included the type of liver resection, demographics, indication for surgery, and average blood loss. Postoperative variables included surgical complications such as bile leak (BL), surgical site infection (SSI), and post-operative hepatic liver failure (PHLF). Patients were also reviewed for length-of-stay (LOS), 30-day mortality, and 90-day mortality rate. Data were collected from the hospital information system (HIS) and analyzed using SPSS 20. Results: A total of 27 patients underwent elective liver resections in the study period. 15 (55.6%) were male and 12 (44.4%) were females. 63% of the patients were less than 60 years with 37% aged ≥ 60. Most common indication for surgery was hepatocellular carcinoma (37%). 44.4% of the cohort underwent segmentectomy, 14.8% underwent sectionectomy and 22.2% underwent right lobectomies whereas 18.5% underwent non-anatomical liver resections. 59.3% of the surgeries were completed laparoscopically, 5 cases were converted to open due to intraoperative complications (conversion rate of 23.8%), and 6 (22.2%) were open liver resections from the start. Mean blood loss was 414 mLs. Post-operative complications were seen in 5 (18.5%) of the patients which included 2 (7.4%) cases of PHLF, 1 (3.7%) case of bile leak, 1 (3.7%) case of SSI with 1 (3.7%) patient requiring relook surgery. Our center had 1 (3.7%) case of 30day mortality due to PHLF and 1 (3.7%) case of 90-day mortality due to disease progression. Conclusions: In conclusion, our study yields comparable results to international standards. This study has several limitations, including a retrospective design and a small sample size. Our newly established HBP department has been working in accordance with the international guidelines to optimize the peri-operative outcomes inspite of being in a resource poor setting and with limited financial capacity.

Objective: To determine the effectiveness of combination of dexamethasone and ondansetron in prevention of postoperative nausea and vomiting in laparoscopic cholecystectomy. Study Design: Descriptive Case Series study. Setting: Departments of Surgery, Khyber Teaching Hospital and Hayatabad Medical Complex, Peshawar. Period: 01 Jan 2018 to 31 May 2019. Material & Methods: A total of 231 patients undergoing laparoscopic cholecystectomies were included in the study and subjected to dexamethasone in combination with ondansetron and followed up at 24 hours after surgery to detect nausea and vomiting. Results: The mean age of the study sample was 38.5 + 10.4 years. In our study, we had 62.3% males and 37.7% female patients. On follow up, we observed that PONV was recorded in 39.4% of patients of which grade 1 were 15.2%, grade 2 were 14.7% and grade 3 were 9.5%. In this regards, the effectiveness of dexamethasone and Ondansetron combination was recorded in 60.6% of patients. Conclusion: The combination of dexamethasone and ondansetron is moderately effective in prevention of post operative nausea and vomiting.