Solution of Fractional Order Differential Equation Problems by Triangular Functions for Biomedical Applications

Abstract—Fractional Order Differential equations are used for modelling of a wide variety of biological systems but the solution process of such equations are quite complex. In this paper Orthogonal Triangular functions and their operational matrices have been used for finding an approximate solution of Fractional Order Differential Equations. This technique has been found to be more powerful in solving Fractional Order Differential Equations owing to the fact that the differential equations are reduced to systems of algebraic equations which are easy to solve numerically and the percentage error is lower compared to other methods of solutions (like: Laplace Transform Method). Also due to the recursive nature of this method, it can also be concluded that this method is less complex and more efficient in solving varieties of the Fractional Order Differential Equations

Diversity and Distribution of Archaea in the Mangrove Sediment of Sundarbans

Mangroves are among the most diverse and productive coastal ecosystems in the tropical and subtropical regions. Environmental conditions particular to this biome make mangroves hotspots for microbial diversity, and the resident microbial communities play essential roles in maintenance of the ecosystem. Recently, there has been increasing interest to understand the composition and contribution of microorganisms in mangroves. In the present study, we have analyzed the diversity and distribution of archaea in the tropical mangrove sediments of Sundarbans using 16S rRNA gene amplicon sequencing. The extraction of DNA from sediment samples and the direct application of 16S rRNA gene amplicon sequencing resulted in approximately 142 Mb of data from three distinct mangrove areas (Godkhali, Bonnie camp, and Dhulibhashani). The taxonomic analysis revealed the dominance of phyla Euryarchaeota and Thaumarchaeota (Marine Group I) within our dataset. The distribution of different archaeal taxa and respective statistical analysis (SIMPER, NMDS) revealed a clear community shift along the sampling stations. The sampling stations (Godkhali and Bonnie camp) with history of higher hydrocarbon/oil pollution showed different archaeal community pattern (dominated by haloarchaea) compared to station (Dhulibhashani) with nearly pristine environment (dominated by methanogens). It is indicated that sediment archaeal community patterns were influenced by environmental conditions