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- ItemAnalytical Solution of Generalized Fractional Integro-Differential Equations via Shifted Gegenbauer Polynomials(Universiti Teknologi Malaysia., 2024-12) Kazeem Issa; Adebayo Ridwan; Muritala Hambali SuleimanIn this paper, we proposed an analytical solution for generalized fractional order integro-differential equations with non-local boundary conditions via shifted Gegenbauer polynomials as an approximating polynomial using the Galerkin method and collocation techniques involving operational matrix that make use of the Liouville-Caputo operator of differentiation in combination with Gegenbauer polynomials. Shifted Gegenbauer polynomial properties were exploited to transform fractional order integro-differential equation and its non-local boundary conditions into an algebraic system of equations. Shifted Gegenbauer polynomial Cm(α)(x) was used in order to generate and generalize the results of some other orthogonal polynomials by varying the value of parameter α. The accuracy and effectiveness of the proposed method are tested on some selected examples from the literature. We observed that, when the exact solution is in polynomial form, the approximate solution gives a closed form solution, and non-polynomial exact solution, also give better results compared to the existing results in the literature.
- ItemUnsteady Radiative Magnetohydrodynamic Flow over a Chemically Reacting Porous Stretching Plate Considering the Soret Effect(2025) Ankur Kumar Sarma; Dipak Sarma; Sunmoni Mudoi; A. Dauda Adeshola; Kazeem Issa; Abdul Azeez Kayode Jimoh; Adebowale Martins ObalaluThe analysis of unsteady MHD flow over a porous stretching plate is critical for various engineering applications, particularly in systems involving chemical reactions and thermal radiation. This study explores the novel effects of heat and mass transfer in a two-dimensional unsteady magnetohydrodynamic (MHD) flow. This present work examines the effects of radiation and a transverse magnetic field on a chemically reacting fluid flowing over a stretched plate. The unsteady nature of the flow is associated with the time-dependent variations in stretching/extending velocity, temperature, and fluid concentration. The nonlinear governing boundary layer partial differential equations (PDEs) are transformed into a set of nonlinear ordinary differential equations (ODEs) using a similarity transformation, which are then numerically solved using the MATLAB bvp4c method. The flow, heat, and concentration profiles are quantitatively analysed through graphs for various problem parameters, including the unsteadiness parameter (A), Hartmann number (M), porosity parameter (Sp), radiation parameter (N), chemical reaction parameter (K), Soret number (Sr), Eckert number (Ec), Schmidt number (Sc), and Prandtl number (Pr). Additionally, the skin friction coefficient, Nusselt number (Nu), and Sherwood number (Sh) are numerically addressed and illustrated using graphs.
- ItemEconomic Selection of Efficient Level of NPK 16:16:16 Fertilizer for Improved Yield Performance of a Maize Variety in the South Guinea Savannah Zone of Nigeria(Journal of Mathematical Theory and Modeling, 2013) Olorede K. O.; Mohammed I. W.; Adeleke B. L.This study investigates effects of different levels of NPK 16:16:16 fertilizer on yield and performance of maize. Data sets were obtained from a study conducted at the University of Ilorin Teaching and Research Farm, faculty of Agriculture, University of Ilorin during the 2010 cropping season. The study was conducted on a maize variety (Swan-1-SR-Y) sourced from Federal Ministry of Agriculture and Water Resources, Abuja, Nigeria using a completely Randomized Design (RCBD) replicated three times. Application of the fertilizer type was done at two equal splits of 2 weeks after planting and immediately after tasseling using ring method of application. The appropriate analysis of variance (ANOVA) model was used to collect observations at 2 weeks interval from week 5 to week 15 after planting on growth variables such as plant height (kg), leaf area (cm2), number of leaves, cob weight (kg) and grain weight (kg) respectively at equally spaced levels 0kg/ha, 30kg/ha, 60kg/ha, 90kg/ha and 120kg/ha of the fertilizer type. Before conducting ANOVA, the data sets were inspected for homogeneity of error variances using Fligner-Killeen test in the R statistical package. Shapiro-Wilk test of normality was used to check normality of the residuals. The normal probability plot showed no indication of outliers and the largest standardized residual was within . NPK 16:16:16 fertilizer level 60 Kg/ha was found to be the most efficient and economical for improving growth and yield performance of the maize variety in the ecological zone. The optimum yield of the maize variety due to application of the NPK 16:16:16 fertilizer levels is in the 13th week after planting.
- ItemPartial Least Squares-Based Classification and Selection of Predictive Variables of Crimes against Properties in Nigeria(Professional Statisticians Society of Nigeria (PSSN), 2017) Olorede K. O.; Yahya W. B.; Garuba A. O.; Banjoko A. W.; Dauda K. A.In this study, the state-of-the-art Partial Least Squares (PLS) based models (PLS-Discriminant analysis (PLS-DA), Sparse PLS-DA (SPLS-DA) and Sparse Generalized PLS (SGPLS)) were employed to model and classify the rate of crimes (low or high) committed against properties across the 36 states in Nigeria and the Federal Capital Territory (FCT). The core variables that are predictive of this crime type in Nigeria were identified using the LASSO penalty method via the PLS. Data on occurrences of cases of offences against property obtained from the data base of Nigerian Police Force were utilized in this study. The missing values due to non-occurrence or non-reportage of crime cases were imputed, using the techniques of multivariate imputation by chained equation. The complete data set were partitioned into training and test sets using 80:20 holdout scheme. The 80% training set was used to build the PLS-based models that were in turn used to predict the overall crime rates of Nigerian cities in the 20% held out test data over 200 Monte-Carlo cross-validation runs. All the PLS-based models yielded good classification of unseen test samples into either of two qualitative classes of high and low crime rates with average Correct Classification Rate (CCR) of 94%. Other performance metrics including sensitivity, specificity, positive and negative predictive values, balance accuracy and diagnostic odds ratio were estimated to further examine their classification efficiencies. The SGPLS identified fewer (just 3 out of 12) core relevant crime variables that are predictive of the overall crime rates in Nigerian states with highest CCR than the SPLS which selected 9 such variables to achieved about the same feat.
- ItemHankel determinants with Fekete-Szegö parameter for a subset of Bazileviˇ c functions linked with Ma-Minda function(PSR Press, 2025-03-29) Lasode, A. O.; Ayinla, R. O.; Bello, R. A.; Amao, A. A.; Fatusin, L. M.; Sambo, Bitrus; Awoyale, O.Consider a unit disk Ω = {z : |z| < 1}. A large subset of the set of analytic-univalent functions defined in Ω is examined in this exploration. This new set contains various subsets of the Yamaguchi and starlike functions, both of which have profound properties in the well-known set of Bazileviˇ c functions. The Ma-Minda function and a few mathematical concepts, including subordination, set theory, infinite series formation and product combination of certain geometric expressions, are used in the definition of the new set. The estimates for the coefficient bounds, the Fekete-Szegö functional with real and complex parameters, and the Hankel determinants with a real parameter are some of the accomplishments. In general, when some parameters are changed within their interval of declarations, the set reduces to a number of recognized sets.