Abstract In this present paper, the effect of fractional analysis on magnetic curves is researched. A magnetic field is defined by the property that its divergence is zero in three dimensional Riemannian manifold. We investigate the trajectories of the magnetic fields called as t-magnetic, n-magnetic and b-magnetic curves according to fractional derivative and integral. As it is known, there are not many studies on a geometric interpretation of fractional calculus. When examining the effect of fractional analysis on a magnetic curve, the conformable fractional derivative that best fits the algebraic structure of differential geometry derivative is used. This effect is examined with the help of examples consistent with the theory and visualized for different values of the conformable fractional derivative. The difference of this study from others is the use of conformable fractional derivatives and integrals in calculations. Fractional calculus has applications in many fields such as physics, engineering, mathematical biology, fluid mechanics, signal processing, etc. Fractional derivatives and integrals have become an extremely important and new mathematical method in solving various problems in many sciences.

Objetivo: Relatamos abordagens clínicas dos departamentos de oftalmologia e otorrinolaringologia para tratar complicações orbitais da sinusite. Uma revisão em profundidade literatura é discutida. Métodos: Foram analisados retrospectivamente os prontuários de 51 pacientes no período de janeiro de 2008 a janeiro de 2014. Os registros foram avaliados quanto à idade, sexo, tipo de complicação orbital, sintomas, fatores predisponentes, estudos de imagem, tratamento médico e cirúrgico, resultados da cultura microbiológica e seguimento. Foi utilizado o programa SPSS versão 15.0 (Statistical Analysis, The Statistical Package for Social Sciences Inc, Chicago, IL) para a análise estatística. Resultados: Cinquenta e um pacientes preencheram os critérios, com os registros médicos disponíveis, para o estudo (29 do sexo masculino, 22 do sexo feminino). Trinta e dois (62,7%) foram diagnosticados com celulite presseptal e 19 (37,3%), com celulite posseptal. Depois de uma avaliação detalhada, 15 foram diagnosticados como abscesso subperiosteal (SPA), 4 eram celulite orbitária. A idade e sexo foi similar para ambos os grupos. Cinco pacientes com abscesso subperiosteal medial foram tratados com cirurgia endoscópica, um paciente com abscessso subperiosteal inferior foi tratado com cirurgia externa, 6 pacientes com outras localizações foram tratados com a combinação de cirurgia endoscópica e cirurgia externo. Todos os pacientes apresentaram eritema e edema periorbital. Tempo de internação hospitalar e a duração dos sintomas foi similar em ambos os grupos. A acuidade visual foi entre 1/10 a 10/10 (média de 7/10) e estatisticamente significante para os grupos celulite presseptal e posseptal (p<0,001). Todos os pacientes receberam antibióticos por via intravenosa, no primeiro dia de admissão. Conclusão: A complicação orbital da sinusite aguda exige um acompanhamento intensivo e multidisciplinar. A tomografia computadorizada dos seios paranasais com contraste pode detectar a extensão da infecção. Uma tentativa inicial com o uso de antibióticos intravenosos é adequada quando um acompanhamento rigoroso é possível. A cirurgia é indicada quando não houver melhora dentro de 48 horas de tratamento clínico, diminuição da acuidade visual (em 8/10) e abscesso não-medial.

Purpose: We reported on the clinical approaches of ophthalmology and otorhinolaryngology departments in the treatment of the orbital complications of sinusitis. We also included an in-depth literature review. Methods: We retrospectively reviewed the medical files of 51 patients from January 2008 to January 2014. The records were evaluated for age, gender, type of orbital complications, symptoms, predisposing factors, imaging studies, medical and surgical management, culture results, and follow-up information. SPSS version 15.0 software (Statistical Analysis, The Statistical Package for Social Sciences Inc, Chicago, IL) was used for the statistical analysis. Results: Fifty-one patients met the criteria, with available medical records, for the study (29 male, 22 female). Thirty-two (62.7%) were diagnosed with preseptal cellulitis and 19 (37.3%) with postseptal cellulitis. After a detailed evaluation, 15 were diagnosed with a subperiosteal abscess (SPA), and 4 were diagnosed with orbital cellulitis. The age and gender was similar for the two groups. Five patients with medial SPA were treated with endoscopic sinus surgery, one patient with inferior SPA was treated with external surgery, and six patients with other localizations were treated with a combination of endoscopic sinus surgery and external surgery. All patients presented with periorbital erythema and edema. The length of hospitalization and duration of symptoms were similar in both groups. Visual acuity was between 1/10 to 10/10 (mean 7/10) and statistically significant for preseptal and postseptal cellulitis groups (p<0.001). All patients received intravenous antibiotics upon the first day of admission. Conclusion: Orbital complications of acute sinusitis required intensive follow-up and a multidisciplinary approach. A contrast-enhanced paranasal sinus computerized tomography (CT) scan can detect the extent of the infection. An initial trial of intravenosus (IV) antibiotics may be appropriate when close monitoring is possible. Surgery may be indicated when there has been no improvement within 48 hours of intravenous treatment, loss of visual acuity (under 8/10), and a non-medial abscess.