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    Condensed Kannan-Type Maps and Their Efficiency Measures in Complete Metric Spaces
    (Kyungpook Mathematical Journal, 2025) Olalekan Taofeek Wahab; Garba Risqot Ibrahim; Salaudeen Alaro Musa
    Recently, some studies introduced interpolative Kannan-type maps for solving non-unique fixed-point problems. However, these studies do not offer a technique for determining the fractional powers of the maps, which would be useful in approximating the fixed points. This study uses two symmetry terms of the conventional Kannan contraction to define a novel condensed Kannan-type contraction in complete metric spaces. By imposing the condensed map on the Picard operator, we prove the existence of unique and non-unique fixed points. We also define a criterion for selecting an appropriate real constant α suitable for approximating the fixed points of the condensed map. We consider two practical and numerical examples to show both the versatility and validity of the hypotheses of this study. These results show that the class of condensed maps is strictly larger than the existing class Kannan-type maps, ensure suitability for solving both unique and non-unique fixed points, and do so with a better convergence rate.
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    Tropical Roots and Their Multiplicities on the Subsemigroup of Order-Decreasing and Order-Preserving Full Transformation
    (Lagos State University (LASU), 2024-12-12) Ibrahim, G. R.; Bakare, G. N.; Usamot, I. F.; Sulyman, O. I.; Akinwunmi, S. A.; Adeshola, A.D.
    Let be ordered finite set. The tropical geometry was utilized to analyze the subsemigroup of order-decreasing and order-preserving semigroups, denoted as full transformation . The elements of classical algebra within were transformed into tropical polynomials, allowing for the determination of tropical roots and their multiplicities through the tropical curve, which was visualized using GeoGebra.
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    Sum-Difference Model for Production of a Star-Like Harmonic Oscillator Transformation Semigroup
    (NIPES Pub., 2025-05-20) Akinwunmi, S. A.; Bakare, G.N.; Ogbu, A.O.; Garba, R.I
    This study introduces a novel sum-difference model for generating a star-like harmonic oscillator transformation semigroup, based on combinatorial properties of partial transformations over the finite set ?? = {1, 2, 3… , ?}. A partial transformation on ?? is defined as a mapping from a subset ?∗ . Using this framework, we construct a generalized two-dimensional star-like harmonic structure to produce ordered sequences and visualizable transformations. Specifically, for transformations ?∗, ?∗, ?∗ ∈ ??? ∗ , the cardinality |??? ∗ | is modeled as 1 2 ??∗ = ??∗−??∗ 2 4?∗?∗ which governs the generation of star-like sequences and image mappings. The paper presents a unified analytical approach to deriving these results using a star-like sumdifference operator. We further establish new harmonic oscillator relations within the semigroup, supported by proofs of key combinatorial functions. This research contributes to the development of algebraic methods in harmonic transformation theory and lays a foundation for future applications in signal modeling, automata theory, and abstract algebraic systems.
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    Analytical Solution of Generalized Fractional Integro-Differential Equations via Shifted Gegenbauer Polynomials
    (Universiti Teknologi Malaysia., 2024-12) Kazeem Issa; Adebayo Ridwan; Muritala Hambali Suleiman
    In 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.
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    Unsteady 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 Obalalu
    The 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.