The aim of this article is to solve the Volterra-Fredholm integro-differential equations of fractional order numerically by using the shifted Jacobi polynomial collocation method. The Jacobi polynomial and collocation method properties are presented. This technique is used to convert the problem into the solution of linear algebraic equations. The fractional derivatives are considered in the Caputo sense. Numerical examples are given to show the accuracy and reliability of the proposed technique.
The term of heterocyclic chemistry focuses only on heterocyclic compounds, which consider as a percentage of organic chemistry, they equal to greater than sixty-five. These compounds are widely founded in nature and most of them are important to life. In the past few years, scientist fused on 1,2,4-triazoles and their condensed heterocyclic ring due to their medicinal significance, 1,2,4-triazole containing Sulphur atom is one of the important heterocyclic moieties due to its broad range of biological activities also their derivatives can accommodate one of the alternatives as electronic effect as exchanges of the electronic density (electron donating or withdrawing) groups ; for all what mentioned above they are consider as a core
... Show MoreThis study aimed to detect antibiotics in water, particulate, plant, and sediment in the Tigris River within Baghdad City, in addition to their spatiotemporal variations, and related physicochemical parameters. Five sites were selected in the river. Three target antibiotics (tetracycline, gentamycin, and ciprofloxacin) were detected in water, particulate, plant, and sediment of the river at all selected sites. The results clearly showed that the concentrations of target antibiotics were sediment > water > plant > particulate. Site 3 is considered as a risk site where high concentrations of all antibiotics during the wet and dry seasons wer
Background/Objectives: Nonsurgical periodontal treatment (NSPT) is the gold-standard technique for treating periodontitis. However, an individual’s susceptibility or the inadequate removal of subgingival biofilms could lead to unfavorable responses to NSPT. This study aimed to assess the potential of salivary and microbiological biomarkers in predicting the site-specific and whole-mouth outcomes of NSPT. Methods: A total of 68 periodontitis patients exhibiting 1111 periodontal pockets 4 to 6 mm in depth completed the active phase of periodontal treatment. Clinical periodontal parameters, saliva, and subgingival biofilm samples were collected from each patient at baseline and three months after NSPT. A quantitative PCR assay was us
... Show MoreNon-steroidal anti-inflammatory drugs (NSAIDs) contain free –COOH which thought to be responsible for the GI irritation associated with all traditional NSAIDs. The esterification of this group is one of an approach to ultimate aim for reduce the gastric irritation; so in this study we synthesized and preliminarily evaluated new ester compounds as new analogues with expected selectivity toward COX-2 enzyme. Synthetic procedures have been successfully developed for the generation of the target compounds (III a and b). The synthetic approach involved multi-steps procedures which include: Synthesis of 4-hydroxy benzene sulphonamide ( I b ), synthesis of Naproxen and Ibuprofen acyl chloride and then reacting them with 4-hydroxy benzene sulphon
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