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

Distribution and sources of linear alkyl benzenes (LABs) in surface sediments from Johor Bahru Coast and the Kim Kim River, Malaysia

This study focuses on sewage pollution, which is one of the most important issues concerning Malaysians. The main location of this study is in Johor Bahru as it is one of the most populated areas in Malaysia. The distribution and sources of linear alkyl benzenes (LABs) were evaluated in surface sediments collected from Johor Bahru Coast and the Kim Kim River, Peninsular Malaysia. The samples were extracted, fractionated and analyzed using gas chromatography-mass spectrometry (GC-MS). This study found that LABs concentrations ranged from 87.6 to 188.7 ng/g dw and 88.2 to 119.02 ng/g dw in surface sediments from Johor Bahru Coast and the Kim Kim River, respectively. Johor Bahru Coast showed an increasing trend of LABs concentrations due to rapid industrialization and population growth. The ratio of internal to external isomers (I/E ratio) of LABs in sediment samples from Johor Bahru Coast ranged from 1.76 to 2.04 while the I/E ratios in sediments from the Kim Kim River ranged from 1.72 to 1.91. All I/E ratios at Johor Bahru Coast and the Kim Kim River stations indicate that the areas were receiving primary and secondary effluents

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

Anthropogenic waste indicators (AWIs), particularly PAHs and LABs, in Malaysian sediments: application of aquatic environment for identifying anthropogenic pollution

Polycyclic aromatic hydrocarbons (PAHs) and linear alkylbenzenes (LABs) were used as anthropogenic markers of organic chemical pollution of sediments in the Selangor River, Peninsular Malaysia. This study was conducted on sediment samples from the beginning of the estuary to the upstream river during dry and rainy seasons. The concentrations of ƩPAHs and ƩLABs ranged from 203 to 964 and from 23 to 113 ng g− 1 dry weight (dw), respectively. In particular, the Selangor River was found to have higher sedimentary levels of PAHs and LABs during the wet season than in the dry season, which was primarily associated with the intensity of domestic wastewater discharge and high amounts of urban runoff washing the pollutants from the surrounding area. The concentrations of the toxic contaminants were determined according to the Sediment Quality Guidelines (SQGs). The PAH levels in the Selangor River did not exceed the SQGs, for example, the effects range low (ERL) value, indicating that they cannot exert adverse biological effects

Distribution of polycyclic aromatic hydrocarbons (PAHs) in sediment from Muar river and Pulau Merambong, Peninsular Malaysia

Previous studies indicated that with increasing industrialization and urbanization, pollution problems have become more significant in Malaysia. West coast of Malaysia is more populated and urbanized than the east and therefore more susceptible to various pollutants. Surface sediment samples were collected from Pulau Merambong and Muar river, Peninsular Malaysia during May 2013 where 16 USEPA Priority Pollutants PAHs were analyzed using gas chromatography-mass spectrometry. Total PAHs in the sediments for Muar river ranged from 15.5 to 165.7 ng/g dw whereas the total PAHs for Pulau Merambong ranged from 38.6 to 122.8 ng/g dw. Due to rapid urbanization and motorization, Muar river showed an increasing trend of PAHs concentrations when compared to a study conducted about a decade ago. Pulau Merambong shows relatively lower PAHs concentrations as compared to other locations in Peninsular Malaysia. However, there is no previous data in Pulau Merambong to evaluate the trend in the petroleum hydrocarbons distribution and concentrations. In general, this study revealed that the lowest concentrations were detected in downstream of the Muar and Pulau Meranbong, respectively. This study also found abundance of high molecular weight (HMW) PAHs as compared to low molecular weight (LMW) PAHs suggesting predominance of pyrogenic PAH sources via atmospheric and long-range input. The ratio of LMW PAHs to HMW PAHs (LMW/HMW) were in the range of 0.05–0.33 indicating pyrogenic input and this is consistent with other diagnostic ratios

Distribution of petroleum hydrocarbons in surface sediments from selected locations in Kuala Selangor River, Malaysia

A study has been conducted at selected locations along the Kuala Selangor River, Malaysia on seven surface sediment samples to determine the level of hydrocarbon pollution in the sediments. The homogenized sediments were extracted using soxhlet, fractionated and analyzed by using GCMS. PAHs were detected and were found in the range of 563–1,037 ng/g (dryweight). Ratio MP/P was used to determine the anthropogenic PAHs sources where seven stations were found to be polluted by petrogenic sources. Furthermore, MP/P ratios for sediment samples had values ranging from 1.752 to 18.6, while L/H ratios for the same samples ranged from 0.2978 to 1.393. There were 26 compounds of PAHs detected in the samples. Further analysis and more data is needed in order to identify the sources of oil pollution in seven sediment samples with unidentified oil sources

Biomass Mediated Synthesis of ZnO and ZnO/GO for the Decolorization of Methylene Blue under Visible Light Source

: In this study, zinc oxide (ZnO) as well as ZnO/GO (zinc oxide/graphene oxide) were successfully synthesized. The Carica papaya leaf extract was used to synthesize ZnO and oil palm empty fruit bunch biomass to obtain graphene, which was further used to obtain graphene oxide. The samples were characterized through a variety of analytical methods such as scanning electron microscopy, transmission electron microscopy, X-ray diffraction analysis, Fourier transform infrared spectroscopy and UV–Visible spectroscopy in order to understand their morphology, size, structural phase purity, functional groups and optical properties. Various peaks such as O-H, Zn-OH and Zn-O were found in the case of ZnO. Some additional peaks, such as C-C and C=C, were also been detected while analyzing the sample by Fourier-transform infrared spectroscopy. The results of the XRD and SEM studies demonstrated that the synthesized material shows the crystalline nature of the substance in the case of ZnO, and the crystallinity decreases for ZnO/GO. The average crystallite size was found to 80.0 nm for ZnO and 74.0 nm for ZnO/GO. Further, a red shift was shown in the case of ZnO/GO, which was indicated by the UV–Vis absorption spectrum. In the TEM analysis, the particles were shown to be nanosized. For instance, the highest number of particles was found in the range of 100 to 120 nm in the case of ZnO, while 80–100 nm sized particles were found for ZnO/GO. Using synthesized ZnO and ZnO/GO, the decolorization of methylene blue was found to be 64% and 91%, respectively

Baseline distributions and sources of polycyclic aromatic hydrocarbons (PAHs) in the surface sediments from the Prai and Malacca Rivers, Peninsular Malaysia

In this study, the surface sediments of the Malacca and Prai Rivers were analyzed to identify the distributions, and sources of Polycyclic Aromatic Hydrocarbons (PAHs). The total PAH concentrations varied from 716 to 1210 and 1102 to 7938 ng g−1 dw in the sediments of the Malacca and Prai Rivers, respectively. The PAH concentrations can be classified as moderate and high level of pollution in the sediments of the Malacca and Prai Rivers, respectively. The comparison of PAHs with the Sediment Quality Guidelines (SQGs) indicates that the PAHs in the sediments of the Malacca and Prai Rivers may have the potential to cause adverse toxicity effects on the sampled ecosystems. The diagnostic ratios of individual PAHs indicate both petrogenic- and pyrogenic-origin PAHs with dominance of pyrogenic source in both rivers. These findings demonstrate that the environmental regulations in Malaysia have effectively reduced the input of petrogenic petroleum hydrocarbons into rivers

Evaluation of distribution and sources of sewage molecular marker (LABs) in selected rivers and estuaries of Peninsular Malaysia

This is the first extensive report on linear alkylbenzenes (LABs) as sewage molecular markers in surface sediments collected from the Perlis, Kedah, Merbok, Prai, and Perak Rivers and Estuaries in the west of Peninsular Malaysia. Sediment samples were extracted, fractionated, and analyzed using gas chromatography mass spectrometry (GC-MS). The concentrations of total LABs ranged from 68 to 154 (Perlis River), 103 to 314 (Kedah River), 242 to 1062 (Merbok River), 1985 to 2910 (Prai River), and 217 to 329 ng g−1 (Perak River) dry weight (dw). The highest levels of LABs were found at PI3 (Prai Estuary) due to the rapid industrialization and population growth in this region, while the lowest concentrations of LABs were found at PS1 (upstream of Perlis River). The LABs ratio of internal to external isomers (I/E) in this study ranged from 0.56 at KH1 (upstream of Kedah River) to 1.35 at MK3 (Merbok Estuary) indicating that the rivers receive raw sewage and primary treatment effluents in the study area. In general, the results of this paper highlighted the necessity of continuation of water treatment system improvement in Malaysia

Distribution and source of hydrocarbons in the sediments of the Selangor River, Malaysia

Environmental pollutants such as anthropogenic hydrocarbons (AHs) are known to result from increased urbanization and act as indicators of anthropogenic activity. Hydrocarbons contamination is a great global concern due to their negative effects on human health and environmental consequences, such as toxic, mutagenic, carcinogenic, teratogenic and hepatotoxic effects. Consequently, a clear understanding and monitoring of distribution, sources, pathways and fate in the environment and ecosystems of AHs is of high importance in sediment samples collected from Kuala Selangor River, which is located on the west coast of Peninsular Malaysia, in order to determine the distributions and sources of hopanes, alkanes, polycyclic aromatic hydrocarbons (PAHs), and linear alkylbenzenes (LABs) in four periods. The sediment samples were collected from the river and its estuary during the rainy inter-monsoonal period, the dry inter-monsoonal period, the North-East Monsoon (NEM) period, and the South-West Monsoon (SWM) period because during these periods the samples are expected to contain varying amounts of pollutants. The collected samples were homogenized, freeze-dried, extracted, cleanup, fractionated and analyzed using gas chromatography mass spectrometry. The results of this study revealed that the concentrations of PAHs for the 13 sampling sites pooled over the four studied periods ranged from 341.33 ng g-1 dw (in the SWM period) to 651.64 ng g-1 dw (in the wet inter-monsoon period) with the mean value of 471.05 ng g-1 dw. In other respects, the outcomes of the one-way ANOVA indicated that the differences between the PAHs among the sampling stations were significant (p < 0.05). The diagnostic ratios of individual PAHs in sediments indicated both petrogenic and pyrogenic origin PAHs with significant dominance of pyrogenic source. The comparison of PAHs with Sediment Quality Guidelines (SQGs) indicates that the levels of the PAHs in the surface sediments of Selangor River are unlikely to cause any adverse biological effects to the aquatic organisms, including those that are closely associated with sediments. No significant correlation was found between AHs and organic carbon, which means that the distribution of AHs was not affected by the organic carbon content. In the four studied periods, the concentrations of the LABs in Selangor River ranged from 23.70 to 113.30 ng g-1 dw with an arithmetical mean of 54.04 ± 22.34 ng g-1 dw. The average concentration of the total LABs was found to be higher in the wet season (65.20 ± 25.04 ng g-1 dw) than in the other seasons. The average values of the ratio of long-chain to short-chain LAB (L/S), C13/C12, and the ratio of Internal to External isomers (I/E) in the sediments of Selangor River during the four studied periods were 2.03 ± 1.06, 1.74 ± 0.28, and 0.6 ± 0.17, respectively, indicating inputs of LABs from direct wastewater discharges. The I/E ratio decreased from upstream to downstream of Selangor River. This indicates that the sedimentary LABs downstream of the river (estuary) were more degraded than those in the upstream. The concentrations of total alkanes (nC10-nC36) ranged from 967 to 3,711 μg g-1 dw in sediment samples. In addition, the results of this study indicated that the alkanes in the sediment samples originated from diverse sources. Fresh oil, terrestrial plants (riverine area), and heavy/degraded oil (estuarine area) were the predominant source of alkanes in sediments. The alkanes originating from higher plants were mostly predominant in sediments from the stations located in upper parts of the river. The levels of hopanes ranged from 235 to 1,044 ng g-1 dw in sediments. The C29/C30 hopanes ratios were similar with those of used crankcase oil and Middle East Crude Oil (MECO), suggesting MECO as a major source of petroleum hydrocarbons (PHCs) in the sediments of Selangor River. In sum, presence of selected hydrocarbons (PAHs, LABs, alkanes, and hopanes) in the sediments of Selangor River, Malaysia, was studied during four periods. The results show that the agricultural, urban, and industrial activities in the state of Selangor, coupled with a high population growth, have caused deterioration in the quality of its river water. The concentrations of the investigated hydrocarbons varied from sampling site to another and from one period to another. Further studies should be conducted to address this problem