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

Chromatographic Separation, Total Determination and Chemical Speciation of Mercury in Environmental Water Samples Using 4-(2-Thiazolylazo) Resorcinol-Based Polyurethane Foam Sorbent-Packed Column

A simple method has been developed for quantitative retention of traces of mercury(II) ions from aqueous media using polyurethane foams (PUFs) loaded with 4-(2-thiazolylazo) resorcinol (TAR). The kinetics and thermodynamics of the sorption of mercury(II) ions onto PUFs were studied. The sorption of mercury(II) ions onto PUF follows a first-order rate equation with k = 0.176 ± 0.010 min−1. The negative values of ΔH and ΔS may be interpreted as the exothermic chemisorption process and indicative of a faster chemisorption onto the active sites of the sorbent. The sorption data followed Langmuir, Freundlich and Dubinin-Radushkevich (D–R) isotherm models. The D-R parameters β, KDR and E were 0.329 mol2 kJ−2, 0.001 μmol g−1 and 1.23 ± 0.07 kJ/mol for the TAR-loaded PUFs, respectively. An acceptable retention and recovery (99.6 ± 1.1%) of mercury(II) ions in water at ≤10 ppb by the TAR-treated PUFs packed columns were achieved. A retention mechanism, involving absorption related to “solvent extraction” and an “added component” for surface adsorption, was suggested for the retention of mercury(II) ions by the used solid phase extractor. The performance of TAR-immobilized PUFs packed column in terms of the number (N), the height equivalent to a theoretical plate (HETP), the breakthrough and critical capacities of mercury(II) ion uptake by the sorbent packed column were found to be 50.0 ± 1.0, 1.01 ± 0.02 mm, 8.75 and 13.75 mg/g, respectively, at 5 mL/min flow rate

Assessment of Sewage Molecular Markers in Port Dickson Coast and Kim Kim River with Sediment Linear Alkylbenzenes

The present study aimed to determine linear alkylbenzenes (LABs) concentrations as organic molecular marker for sewage pollution in the sediment samples collected from Coast of Port Dickson and Kim Kim River, Peninsular Malaysia. The adverse effects of anthropogenic inputs into the rivers and coastal environment could be detected by molecular organic markers such as LABs. The sediments were processed; their sources were identified and tested by gas chromatography-mass spectrometry (GC-MS). The significance of the differences among sampling stations for LAB concentrations and distribution at p < 0.05 was performed by analysis of variance and Post Hoc Tests, LSD procedures (ANOVA) and Pearson correlation coefficient. LABs indices which include internal to external (I/E) congeners, long to short chains L/S and homologs C13/C12 were used to identify the sewage treatment and degradation levels. Results of this study are statistically uncovered that the range of RLABs concentration in the investigated locations was between 112.0; 88.3 and 256.0; 119.0 ng�g1 dw, respectively. There was significant difference (p < 0.05) of LAB homologs with high percentage of C13-LAB homologs along sampling locations. The calculated LAB ratios (I/E) were within the range between 2.0; 1.7 and 4.1, 2.0, demonstrated that, the treated effluents from primary and secondary sources were discharged to the study areas. The degradation of LABs was 40–64% and 34–38% in the studied locations. The findings of this study suggested the powerfully indicators of LABs in tracing anthropogenic sewage contamination and the necessity of continuing wastewater treatment system improvemen

Green synthesis of mesoporous 2D Mn2O3/rGO nanocomposite for effective removal of methyl orange

Green synthesis of di-manganese trioxide mesoporous structure (super nano porous) sheets (Mn2O3-rGO-NS), Graphene oxide nano sheets (GO) and Mn2O3-rGO-NS nano sheets composite (Mn2O3-rGO-NS) were prepared via Thermal decomposition, seconds timescale water electrolytic oxidation and sonication method respectively. The prepared samples were characterized via X-ray diffraction, FESEM, TEM , and FTIR. Average crystallite size was found about 38 and 26 nm for Mn2O3-NS and Mn2O3-rGO-NS, respectively. Mn2O3-rGO–NPs morphology reveal nano porous sheets within average 35 nm and 26 nm in pores diameter and thickness respectively. Mn2O3-NS act distributed on and between graphene sheets creating macro and nano pores. The obtained results showed that the characteristics of the α-Mn2O3-rGO-NS sheets were improved by the addition of rGO sheets. Methyl orange (MO) dye adsorption onto Mn2O3-rGO-NS composite was investigated at various adsorption parameters, including pH, adsorbent quantity, and time. It was discovered that the adsorption behavior complies with the intra-particle diffusion model and the Friedendlich isotherm. Methyl orange in aqueous media may be eliminated 99.3% by Mn2O3-rGO-NS composite. HIGHLIGHTS Mesoporous graphene-based composite synthesis for dye removal from aqueous media with high efficiency and capacity. According to thermodynamics and kinetics adsorption is favorable, which opens up the possibility for further trials on various types of pollutant removal studies for the industry.

Assessment of Sewage Molecular Markers in Port Dickson Coast and Kim Kim River with Sediment Linear Alkylbenzenes

The present study aimed to determine linear alkylbenzenes (LABs) concentrations as organic molecular marker for sewage pollution in the sediment samples collected from Coast of Port Dickson and Kim Kim River, Peninsular Malaysia. The adverse effects of anthropogenic inputs into the rivers and coastal environment could be detected by molecular organic markers such as LABs. The sediments were processed; their sources were identified and tested by gas chromatography-mass spectrometry (GC-MS). The significance of the differences among sampling stations for LAB concentrations and distribution at p < 0.05 was performed by analysis of variance and Post Hoc Tests, LSD procedures (ANOVA) and Pearson correlation coefficient. LABs indices which include internal to external (I/E) congeners, long to short chains L/S and homologs C13/C12 were used to identify the sewage treatment and degradation levels. Results of this study are statistically uncovered that the range of RLABs concentration in the investigated locations was between 112.0; 88.3 and 256.0; 119.0 ng�g1 dw, respectively. There was significant difference (p < 0.05) of LAB homologs with high percentage of C13-LAB homologs along sampling locations. The calculated LAB ratios (I/E) were within the range between 2.0; 1.7 and 4.1, 2.0, demonstrated that, the treated effluents from primary and secondary sources were discharged to the study areas. The degradation of LABs was 40–64% and 34–38% in the studied locations. The findings of this study suggested the powerfully indicators of LABs in tracing anthropogenic sewage contamination and the necessity of continuing wastewater treatment system improvement