In this paper, the Klein - Gordon equation is generalized using the
concept of the variational order derivative. We try to construct the Crank-
Nicholson scheme for numerical solutions of the ...modified Klein- Gordon equa-
tion. Stability analysis of the Crank-Nicholson scheme is examined and ana-
lyzed to prove the proposed method is stable for solving the time-fractional
variable order Klein- Gordon equation. Numerical examples are also given for
illustration.
In this work, the newly developed optimal perturbation iteration technique with Laplace transform is applied to the generalized regularized long wave equations with a new fractional operator to ...obtain new approximate solutions. We transform the classical generalized regularized long wave equations to fractional differential form by using the Atangana-Baleanu fractional derivative which is defined with the Mittag-Leffler function. To show the efficiency of the proposed method, a numerical example is given for different values of physical parameters.
•The model of polluted lake system is introduced in a short way.•Fractional type of polluted lake system is constructed.•Modified model is analyzed in detail with Atangana–Baleanu derivative.•A ...numerical example is given to demonstrate the efficiency of the newly proposed operator.
In this paper, we use Atangana–Baleanu derivative which is defined with the Mittag–Leffler function and has all the properties of a classical fractional derivative for solving the system of fractional differential equations. The classical model of polluted lakes system is modified by using the concept of fractional differentiation with nonsingular and nonlocal fading memory. The new numerical scheme recommended by Toufik and Atangana is used to analyze the modified model of polluted lakes system. Some numerical illustrations are presented to show the effect of the new fractional differentiation.
Objectives: Accessory spleen, also known as “splenule”, is the presence of splenic tissue in ectopic localisations. The presence of splenule is important, especially in patients planned for ...splenectomy, as it may cause refractory symptoms. The aim of the present study is to define the frequency of splenule(s) in children (0-17 years) who received non-contrast and contrast enhanced computed tomography (NECT and CECT) protocols in the emergency department.
Material and methods: 748 children (aged 0 to 17 years) who were admitted to the emergency department between May 2015 – September 2022 and had NECT and CECT abdominal scans were included in the study. Patients whose CT protocols were incomplete and cases with traumatic splenic injury and / or cases with poor image quality and patients with a history of splenectomy or hematologic pathology were excluded from the study (n: 100). A total of 648 patients were included in the cohort. NECT and CECT scans of all patients were assessed; the localisation of splenules as well as the antero-posterior (AP), medio-lateral (ML) and cranio-caudal (CC) dimensions of each splenule were measured.
Results: A total of 648 cases with 467 males (72.1%) and 181 females (27.9%) were included in the study. Splenules were observed in 131 (20.2%) cases. More than one splenule was observed in 21 of these 131 cases. A total number of 159 splenules were observed in total, with a mean volume of 0,72 ±0,95 ml. The most common location was found to be the splenic hilus (n=55, 41.9%).
Conclusion: Our study have stated that splenules are common anatomical variants, seen at a rate of 20,2% in this age cohort. A cross-sectional imaging should be performed to determine the presence, location, and number of the splenules before a planned splenectomy.
Amaç: Aksesuar dalak olarak ta bilinen splenül, dalak dokusunun ektopik lokaizasyonlarda bulunmasıdır. Özellike cerrahi planlanacak hastalarda splenül varlığının tayini önem teşkil etmektedir. Çalışmamızın amacı acil service başvuran kontrastlı ve kontrastsız bilgisayarlı tomografi (BT) çekimi yapılan çocuklarda (0-17 yaş) splenül sıklığını belirlemektir.
Gereç ve Yöntemler: Mayıs 2015 – Eylül 2022 tarihleri arasında acil servise başvuran ve batın BT ile tetkik edilen 748 çocuk hasta içerisinden çekim protokolü eksiği olan, travmatik dalak hasarı olan veya hematolojik hastalık öyküsü olan olgular çalışma dışı bırakılarak (n: 100) toplam 648 olgu çalışmaya dahil edildi. BT görüntüleri gerek splenül lokalizasyonu gerekse hacimleri açısından incelendi.
Bulgular: Çalışmaya 467 erkek (%72.1) ve 181 kadın (%27.9) oldu arasından 131 olguda (%20.2) splenül tespit edildi. Splenül tespit edilenlerde erkek / kız oranı 3/1 idi. 21 olguda birden fazla splenül tespit edildi. Toplamda 159 splenül izlenmiş olup tespit edilen splenüllerin ortalama hacmi 0.72 ±0.95 ml ve en sık yerleşim yeri dalak hilusu (n=55, %41.9) olarak tespit edildi.
Sonuç: Çalışmamız sık bir anatomik varyant olan splenül’ün çocuk yaş grubunda %20 oranında görüldüğünü göstermiştir. Bu kadar sık görülen bir anatomik varyantın tedavi amacıyla splenektomi planlanan çocuk hasta grubunda operasyon öncesinde mutlaka görüntüleme ile mümkünse kesitsel görüntüleme ile splenül varlığı, lokalizasyonu ve adeti belirlenmesi önerilir.
In this paper, we examine a cubic isothermal auto-catalytic chemical system (CIACS) with the help of the newly developed technique. Classical model of this system is transformed into a new fractional ...forms by using three different and special fractional operators. The new model is therefore called as fractional cubic isothermal auto-catalytic chemical system (FCIACS). Then, the new systems are solved by optimal perturbation iteration method. Obtained results are compared to get an idea about the new derivative operators and optimal perturbation iteration method.
Purpose
To demonstrate feasibility and safety of ultrasound-guided popliteal sciatic nerve block for providing analgesia during urgent endovascular treatment of critical limb ischemia with resting ...pain.
Materials and Methods
Ultrasound-guided popliteal sciatic blocks were performed by an interventional radiologist in angiography suite immediately prior to commencement of urgent endovascular treatment of 30 critical limb ischemia patients. Subjective pain levels prior to and following sciatic block were assessed using the visual analog scale (VAS). Need for any supplemental anxiolytics or analgesics during treatment was recorded. Post-procedural evaluation of patient and operator satisfaction levels regarding the intervention was also documented.
Results
Ultrasound-guided sciatic block provided adequate analgesia in all patients; VAS scores were 0 (no pain) in 87% and 1–3 (mild to annoying pain) in 13%. Two patients required anxiolytic premedication. Additional analgesia was not required during course of endovascular treatment of any patients. Time necessary to perform sciatic block ranged 3–9 (mean 5.9 ± 1.3) min. Median number of needle attempts was 1 (range 1–3). Onset of satisfactory block ranged from 5 to 20 min (mean 9.4 ± 2.6 min). Mean treatment time was 102.2 ± 36.7 min, and balloon time was 22.4 ± 6.1 min. Patient and operator satisfaction with pain control were very good in all cases. There were no procedure-related complications.
Conclusions
Ultrasound-guided popliteal sciatic block is a feasible and safe alternative for providing adequate analgesia during urgent endovascular treatment of critical limb ischemia with resting pain.
Level of Evidence
Level 4, case series.
Ebola virus disease is a fatal hemorrhagic fever of humans and primates caused by viruses. There are many mathematical models to investigate this viral disease. In this paper, the classical form of ...the Ebola virus disease model has been modified by using new fractional derivatives. The resulting fractional forms of the Ebola virus disease model have then been examined by applying a newly-developed semi-analytical method. The optimal perturbation iteration method has been implemented to obtain new approximate solutions to the system of differential equations which better model the Ebola virus disease. New algorithms are constructed by using three types of operators of fractional derivatives. A real-world problem is also solved in order to prove the efficiency of the proposed algorithms. A good agreement has been found with the real values of the parameters. Finally, several graphical illustrations are presented for different values of the involved biological parameters to show the effects of the new approximate solutions. Obtained results prove that the new method is highly accurate in solving these types of fractional models.
In this paper, we introduce the new optimal perturbation iteration method based on the perturbation iteration algorithms for the approximate solutions of nonlinear differential equations of many ...types. The proposed method is illustrated by studying Bratu-type equations. Our results show that only a few terms are required to obtain an approximate solution which is more accurate and efficient than many other methods in the literature.
In this paper, the new optimal perturbation iteration method has been applied to solve the generalized regularized long wave equation. Comparing the new analytic approximate solutions with the known ...exact solutions reveals that the proposed technique is extremely accurate and effective in solving nonlinear wave equations. We also show that,unlike many other methods in literature, this method converges rapidly to exact solutions at lower order of approximations. KCI Citation Count: 17
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