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In this paper, for the first time, the distributed‐order time‐fractional forced Korteweg–de Vries equation is studied. We use a numerical method based on the shifted Legendre operational matrix of distributed‐order fractional derivative with Tau method to find approximate solution of distributed‐order forced Korteweg–de Vries equation. This shifted Legendre operational matrix of distributed‐order fractional derivative with Tau method is used to reduce the solution of the distributed‐order time‐fractional forced Korteweg–de Vries equations to a system of algebraic equations. An error analysis and convergence are obtained. Finally, to display the applicability and validity of the numerical method, some examples are implemented. [ABSTRACT FROM AUTHOR]

In this paper, we use Chebyshev polynomials to seek the numerical solution of a class of multi-variable order fractional differential equation (MVODEs) that the fractional derivative is described in the Caputo-Prabhakar sense. Using operational matrices, the original equations are transferred to a system of algebraic equations. By solving the system of equations, the numerical solutions are acquired that this system may be solved numerically using an iterative algorithm. The effectiveness and convergence analysis of the numerical scheme is illustrated through four numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the regular and singular fractional Sturm-Liouville problem (SLP) where the operator is the Weber fractional derivative of order α. We show then the eigenvalues of fractional SLP are real and the eigenfunctions corresponding to distinct eigenvalues are orthogonal. We also consider a Jacobi type singular fractional SLP and treat the behaviours of its eigenvalues. We further introduce the finite fractional Fourier transform and use this transform for solving the space-fractional diffusion equation problem. [ABSTRACT FROM AUTHOR]

Background: Upper gastrointestinal cancer is the most common cancer in Ardabil Province, North-West of Iran, accounting for more than 50% of all cancer deaths in this area. We conducted this study to determine the present survival rate of patients with esophageal and gastric cancers before launching interventional studies., Methods: A prospective follow-up study of 420 biopsy-proven patients (127 females, mean age: 64) with upper gastrointestinal cancer (141 esophageal and 279 stomach cancers) who were initially diagnosed in Aras Clinic, the main gastrointestinal referral center of Ardabil Province, from 2000 through 2004, was performed with collection of data on demographics, tumor characteristics, pathologic stage, treatment methods, complications, survival time, etc. Data were gathered through direct interview with patients or their families in 303 cases and evaluation of death certificates in 55 patients. Follow-up was from cancer diagnosis until death, or immigration. Survival according to stage of disease, Lauren tumor type, tumor location, surgery, and adjuvant chemotherapy was analyzed, and results were compared with those of western series., Results: Sixty-two cases were lost to follow-up. The one- and five-year survival rates in the patients with upper gastrointestinal cancer in Ardabil Province were 40.5%, and 0.8%, respectively. In the univariate analysis, men had a slightly lower survival rate than women (P = 0.21) and patients with esophageal cancer had a longer survival rate compared to stomach cancer patients (P = 0.15). Patients who had undergone surgery (P < 0.001) and/or chemotherapy (P < 0.001) survived longer than those without such treatments. Tumor morphology, age at diagnosis, radiotherapy, alcohol, and opium consumption did not show any significant effects on the survival rate of patients. In multivariate analysis, only smoking was remained as an independent factor for stomach cancer (P = 0.04) while in esophageal cancer, surgery and grade of differentiation were significant predictors of survival., Conclusion: Survival rate of stomach and esophagus cancer cases in Ardabil is relatively low. Intervention for early detection and therapy is necessary to increase survival.

Aim: Both observational and experimental studies have shown that higher selenium status reduces the risk of upper gastrointestinal cancers in selenium deficient populations. Recent cancer registry data have shown very different rates of esophageal cancer (EC) and gastric cancer (GC) in four Provinces of Iran, namely Ardabil, Mazandaran, Golestan, and Kerman. The aim of this study was to have a preliminary assessment of the hypothesis that high rates of EC in Golestan and high rates of GC in Ardabil may be partly attributable to selenium deficiency., Methods: We measured serum selenium in 300 healthy adults from Ardabil (n = 100), Mazandaran (n = 50), Golestan (n = 100), and Kerman (n = 50), using inductively coupled plasma, with dynamic reaction cell, mass spectrometry (ICP-DRC-MS) at the US Centers for Disease Control (Atlanta, Georgia)., Results: The median serum selenium concentrations were very different in the four Provinces. The medians (IQR) for selenium in Ardabil, Mazandarn, Golestan, and Kerman were 82 (75-94), 123 (111-132), 155 (141-173), and 119 (110-128) microg/L, respectively (P<0.001). The results of linear regression showed that the Province variable, by itself, explained 76% of the variance in log selenium (r2 = 0.76). The proportion of the populations with a serum selenium more than 90 microg/L (the concentration at which serum selenoproteins are saturated) was 100% in Golestan, Kerman, and Mazandaran but only 29% in Ardabil., Conclusion: Our findings suggest that selenium deficiency is not a major contributor to the high incidence of EC seen in northeastern Iran, but it may play a role in the high incidence of GC in Ardabil Province., (Copyright 2004 The WJG Press ISSN)