Global Impact Journal: Advances in Mathematical Physics

Numerical Investigation of Fractional Third-Order Differential Equation Using Quartic B-Spline Functions

Syeda Alishba Batool — 2026-05-13

Fractional calculus (FC) has become more popular during the past four decades due to its extensive applications in mathematics, physics, engineering, and statistics. B-spline functions offer ﬂexible and incredibly precise approximations because of their piecewise polynomial structure and smoothness at knots. For a class of third-order conformable boundary value problems (BVPs), we develop approximation solutions using the quartic B-spline method. The conformable fractional derivative (CFD) is utilized to formulate fractional problems. More speciﬁcally, singularities are used to modify the category of conformable Lane Emden models. Three numerical examples are shown and examined to demonstrate the approach’s effectiveness. The numerical results are highly accurate and require less computational work, and they closely match the exact solutions.

Multiphysics Finite Element Analysis of Diffusive–Bioconvective MHD Hybrid Nanofluid Flow Over an Exponentially Stretching Sheet

Paul M. Matao — 2026-08-27

This study examines the diffusive–bioconvective magnetohydrodynamic (MHD) flow of a hybrid nanofluid past an exponentially stretching sheet embedded in a porous medium, incorporating thermal radiation, viscous dissipation, Soret–Dufour effects, and gyrotactic microorganisms. The hybrid nanofluid, consisting of nanoparticles (Ag+TiO₂) suspended in water, is employed to enhance thermal conductivity and overall heat transfer performance. The governing nonlinear partial differential equations for the incompressible, steady, and two-dimensional flow are transformed into a system of ordinary differential equations via appropriate similarity variables and solved numerically using the finite element method (FEM). Comprehensive parametric analyses reveal that the fluid velocity decreases with increasing magnetic field strength and suction parameter, while it rises under the influence of viscous dissipation, thermal radiation, and the Dufour effect. The temperature field is significantly augmented by thermal radiation, viscous dissipation, and coupled Soret–Dufour mechanisms. The concentration field diminishes
with stronger chemical reactions and higher Lew is numbers but grows with the Soret effect. Furthermore, skin friction coefficient increases notably with magnetic field intensity, viscous dissipation, and Soret–Dufour parameters. Both the local Nusselt number and Sherwood number exhibit declining trends with rising heat generation and chemical reaction rate, respectively. The computed results demonstrate excellent agreement with established benchmark solutions.

Mass Transport Analysis in an Annular Microchannel Driven by a Time-Periodic Oscillatory Electroosmotic Flow for a Maxwell Fluid Under High Zeta Potential

Yuran Qiao — 2026-08-06

This study investigates characteristics of the mass transport for Maxwell ﬂuids driven by a time-periodic oscillatory electroosmotic ﬂow (EOF) in annular microchannels under high zeta potential conditions. A ﬁnite difference method is employed to solve the nonlinear Poisson–Boltzmann equation, the Maxwell ﬂuid momentum equation, the convection–diffusion equation, and the time- and space-averaged mass transport rates are obtained by using the composite trapezoidal rules, and the reliability of the present numerical results for the low zeta potential is veriﬁed by comparing the analytical approximate results obtained by using the Debye–Hückel (D–H) linear approximation. The effects of key dimensionless parameters—including electrokinetic width, angular Reynolds number, wall potential ratio, relaxation time, and the inner-to-outer radius ratio—on ﬂow velocity, solute concentration distribution, and average mass transport performance are systematically analyzed. The results show that: (1) a high zeta potential enhances velocity and concentration, while suppressing the spatio-temporal average mass transport rate; (2) the elastic effects of Maxwell ﬂuids, characterized by relaxation time, signiﬁcantly modulate the structure of velocity and concen-tration ﬁelds under periodic electric forcing, thereby enhancing local mixing or enabling spatially selective separation; (3) at low Reynolds number, the ﬂow remains relatively uniform, facilitating species separation, whereas at higher Reynolds number, ampliﬁed elastic responses near the walls lead to increased nonuniformity in velocity and concentration distributions, promoting mixing; (4) asymmetric zeta potentials induce elastic responses in the core region, further intensifying concentration nonuniformity and enabling species separation under speciﬁc parameter combinations; and (5) geometric factors such inner-to-outer radius ratio and electrokinetic width signiﬁcantly affect radial gradient intensity, resulting in switching phenomena between fast- and slow-diffusing species.

Dynamical Behavior and Chaotic Nature of M-Fractional Paraxial Wave Equation With Three Analytical Methods

Md. Mamunur Roshid — 2026-08-27

This research work provides a comprehensive investigation of the M-fractional paraxial wave equation (M-fPWE) in describing complex optical phenomena in telecommunication systems and nonlinear media, focusing on the dynamical analysis of optical soliton solutions, the impact of M-fractional parameters, stability, multistability, and the chaotic nature of the proposed model. To examine optical soliton solutions for the time M-fPWE model, we employ three advanced analytical methods, such as the Exp_a-function, improved Kudryashov, and uniﬁed solver techniques. These methods yield diverse soliton structures, such as the Exp_a-function technique, which produces kinky periodic waves, kink, and anti-kink waves, and double periodic waves; the improved Kudryashov method reveals solitary periodic waves, kink, and periodic waves, various periodic breather waves, and interactions such as kink-periodic lump and anti-kink periodic lump waves; the uniﬁed solver technique uncovers double periodic waves, periodic breather waves, and kink-bell shape interactions. Moreover, by employing the Galilean transformation, we formulated the dynamical system of the equation, facilitating a comprehensive chaotic analysis, 2D and 3D phase portraits, Poincaré plots, and multistability analysis that uncovered essential data transmission systems. Finally, we compare our results and outcomes with a published work. The obtained results are signiﬁcant in understanding key physical phenomena in optical ﬁber communication.

Thermal Radiative Flow and Entropy Generation in MHD Williamson Hybrid Nanoﬂuid (Cu+Ag)/H2O Over a Porous Stretching Sheet With Non-Fourier Heat Flux and Heat Source

Tigabu Gubena — 2026-08-27

This study investigates the radiative magnetohydrodynamic (MHD) flow of Williamson and hybrid Williamson nanofluids (Cu–water and Cu + Ag–water) over a porous, linearly stretching sheet with suction and internal heat generation. Although nanofluids have been extensively studied, limited research addresses the combined influence of non-Fourier heat flux, viscous dissipation, thermal radiation, and entropy generation in Cu + Ag/water Williamson hybrid nanofluids. The novelty of this work lies in its comprehensive analytical modeling of these coupled transport phenomena and in providing a comparative assessment between Cu–water and Cu + Ag–water Williamson nanofluids under realistic boundary conditions. The governing nonlinear equations are reduced using similarity transformations and solved analytically through the Homotopy Analysis Method (HAM), which offers excellent convergence control for highly nonlinear systems. Results show that the Cu–water nanofluid exhibits higher velocity due to lower viscosity, while the Cu + Ag–water hybrid nanofluid demonstrates superior thermal conductivity and enhanced heat transfer. The wall shear (skin friction) increases with We but decreases with M, K, and S, reflecting the competing roles of elastic effects versus magnetic braking, porous drag, and suction-induced momentum reduction. Meanwhile, the Nusselt number decreases with M, K, and Q, but increases with Nr, S, and γ, indicating that radiative transport, boundary-layer thinning, and thermal relaxation steepen − θ'(0), thereby offering a concise guideline for balancing heat-transfer enhancement against frictional penalties. An increase in the thermal relaxation parameter (γ) delays the heat-flux response in the Cattaneo–Christov model, which weakens thermal diffusion, lowers the boundary-layer temperature, and improves thermal stability. As a result, the wall temperature gradient steepens, increasing − θ'(0) and enhancing the Nusselt number. Entropy generation is intensified by the magnetic parameter (M), porous resistance (permeability) parameter (K), and Brinkman number (Br), but it is suppressed by the Weissenberg number (We) and temperature-difference effects. Overall, the findings provide valuable insight for optimizing hybrid nanofluid-based systems in cooling, micro-electro-mechanical systems (MEMS), and sustainable thermal management applications.