Wavelets operational methods for fractional differential equations and systems of fractional differential equations

In this thesis, new and effective operational methods based on polynomials and wavelets for the solutions of FDEs and systems of FDEs are developed. In particular we study one of the important polynomial that belongs to the Appell family of polynomials, namely, Genocchi polynomial. This polynomial has certain great advantages based on which an effective and simple operational matrix of derivative was first derived and applied together with collocation method to solve some singular second order differential equations of Emden-Fowler type, a class of generalized Pantograph equations and Delay differential systems. A new operational matrix of fractional order derivative and integration based on this polynomial was also developed and used together with collocation method to solve FDEs, systems of FDEs and fractional order delay differential equations. Error bound for some of the considered problems is also shown and proved. Further, a wavelet bases based on Genocchi polynomials is also constructed, its operational matrix of fractional order derivative is derived and used for the solutions of FDEs and systems of FDEs. A novel approach for obtaining operational matrices of fractional derivative based on Legendre and Chebyshev wavelets is developed, where, the wavelets are first transformed into corresponding shifted polynomials and the transformation matrices are formed and used together with the polynomials operational matrices of fractional derivatives to obtain the wavelets operational matrix. These new operational matrices are used together with spectral Tau and collocation methods to solve FDEs and systems of FDEs

Seasonal variability of anthropogenic indices of PAHs in sediment from the Kuala Selangor River, west coast Peninsular Malaysia

Rapid increase in industrialization and urbanization in the west coast of Peninsular Malaysia has led to the intense release of petroleum and products of petroleum into the environment. Surface sediment samples were collected from the Selangor River in the west coast of Peninsular Malaysia during four climatic seasons and analyzed for PAHs and biomarkers (hopanes). Sediments were soxhlet extracted and further purified and fractionated through first and second step column chromatography. A gas chromatography–mass spectrometry (GC–MS) was used for analysis of PAHs and hopanes fractions. The average concentrations of total PAHs ranged from 219.7 to 672.3 ng g−1 dw. The highest concentrations of PAHs were detected at 964.7 ng g−1 dw in station S5 in the mouth of the Selangor River during the wet inter-monsoonal season. Both pyrogenic and petrogenic PAHs were detected in the sediments with a predominance of the former. The composition of hopanes was homogeneous showing that petroleum hydrocarbons share an identical source in the study area. Diagnostic ratios of hopanes indicated that some of the sediment samples carry the crankcase oil signature

Assessment of Sewage Molecular Markers: Linear Alkylbenzenes in Sediments of an Industrialized Region in Peninsular Malaysia

In this study, the use of linear alkylbenzenes (LABs) was employed to pinpoint the sources of human activity that cause detrimental impacts on the coastal environment and river ecosystems. LABs were detected using GC–MS in sediment samples assembled from Kim Kim River (KKR) and the Port Dickson coast (PDC). To assess the significance of variations in the distribution and concentrations of LABs across the sampling sites, this study utilized several statistical techniques such as post hoc tests, LSD techniques, analysis of variance (ANOVA), and the Pearson correlation coefficient using a significance level of p 13 and C12, and long-to-short-chain (L/S) ratios. The results revealed that the LAB concentrations varied between 88.3 and 112 ng/g dw in KKR and 119 to 256 ng/g dw in the PDC. Most of the surveyed areas exhibited a substantial count of C13–LABs homologs that displayed a significant difference (p < 0.05). The I/E ratios ranged from 1.7 to 2.0 in KKR and from 2.0 to 4.1 in the PDC, suggesting that the effluents originated from sources associated with the physical phase and biological phase in wastewater treatment systems (WWTSs). The results revealed that the degradation of LABs varied between 34% and 38% in KKR and between 40% and 64% in the PDC. This study underscores the importance of ongoing improvements to WWTSs and emphasizes the potential of LABs as indicators for monitoring wastewater contamination