We study travelling-wave solutions of the generalized Sharma-Tasso-Olver (GSTO) equation $u_t+\lambda(u^{r})_x+\mu(u^{s})_{xx}+\nu u_{xxx}=0$, in which the exponents $r,s>0$ need not be integers. The classical, modified and generalized Kudryashov methods are applied to the reduced ordinary differential equation. A balance argument shows that the convective term fixes the degree of the expansion through $N=2/(r-1)$, whereas the nonlinear diffusion term requires $N=1/(s-1)$; the two requirements are compatible only when $r=2s-1$, a condition satisfied by the classical STO equation ($r=3$, $s=2$). For the representative non-integer cases $(r,s)=(2,\tfrac32)$ and $(\tfrac32,2)$ we show that boun... More >

This study formulates a mathematical and computational model of tumor-cell-density regression in pancreatic cancer treated with carbon-ion hadron therapy. A reaction-diffusion equation with logistic proliferation and a local radiation-induced loss term is derived term by term, discretized with a two-dimensional finite-difference scheme and forward Euler time stepping, and implemented in Python. The treatment input follows a published carbon-ion schedule of 48~Gy(RBE) in 12 fractions of 4~Gy(RBE). The simulation produces sequential two- and three-dimensional maps of the modeled tumor-cell density as a function of accumulated dose; in the three-dimensional reconstruction the relative tumor vo... More >

Corporate carbon abatement is commonly modeled as a direct and continuous response to environmental regulation or green innovation. Such representations cannot fully explain persistent differences among firms facing similar policy conditions or distinguish the pressure required to initiate a low-carbon transition from that needed to sustain it. This study develops a three-state continuous-time model linking corporate carbon abatement, accumulated green innovation, and effective regulatory pressure, with green market preference treated as an external demand-pull parameter. Green innovation lowers the marginal cost of abatement, abatement generates learning and commercial returns to innovation... More >

In this study, a compartmental mathematical model is developed to study the rabies transmission process from dog to human. The model consists of eight compartments: susceptible, exposed, infected, recovered groups for dogs and humans $(S_D, E_D, I_D, R_D, S_H, E_H, I_H, R_H)$. The basic reproduction number $R_0$ is derived, and sensitivity analysis is performed to identify the most influential epidemiological parameters. Disease-free equilibrium stability analysis is also carried out to identify the conditions for rabies eradication. One of the main goals of this work is to compare the disease dynamics in vaccinated and unvaccinated cases, which is carried out with the support of numerical s... More >

This study develops a mathematically explicit and computationally reproducible framework based on the delayed Mackey--Glass equation for leukemia-related population dynamics. The classical model is formulated from a population balance law, delayed maturation, and saturating nonlinear feedback, and is then extended by a stage-dependent treatment-control term. Parameters that are not identifiable from the available clinical information are taken from established mathematical and hematopoietic literature, while the treatment-control coefficients are constrained phenomenologically by the modeled burden states. A brief systematic literature search was used to characterize previous Mackey--Glass a... More >

This paper investigates the combined effects of magnetohydrodynamics (MHD), double-diffusive convection, radiative heat transfer, and viscous dissipation in a porous wavy cavity. The Darcy–Forchheimer model and Rosseland approximation are employed; the dimensionless governing equations are solved using the Galerkin finite element method with triangular elements. Key quantitative findings include: the Hartmann number suppresses convective transport, reducing average Nusselt and Sherwood numbers by up to 59% at $Ha=50$; the radiation parameter $N_1$ enhances heat transfer by 169% as $N_1$ varies from 0.01 to 10; viscous dissipation paradoxically reduces wall heat flux by 33% despite increasi... More >

Stiff systems of ordinary differential equations (ODEs) arise frequently in science, engineering, and applied mathematics, and their numerical solutions require methods with strong stability properties to avoid severe step-size restrictions. This motivates the development of efficient and stable numerical schemes tailored for such problems. In this paper, a fully implicit hybrid block method, termed the Two-Point Superclass Block Backward Differentiation Formula with Off-step Points (2SBBDFO), is proposed for solving stiff ODE systems. The method extends the classical two-point block BDF by incorporating a non-zero coefficient $\beta_{k-1}$, enabling the simultaneous computation of two grid-... More >

In this study, the New Iteration Method (NIM) is employed to obtain approximate analytical solutions of nonlinear fourth-order ordinary differential equations of the general form \[ \mathcal{L}(u) + \mathcal{N}(u) = g(x), \qquad x \in [a,b], \] subject to the two-point boundary conditions \[ \mathcal{B}_1(u)=0, \qquad \mathcal{B}_2(u)=0, \] where $\mathcal{L}$ denotes a linear differential operator, $\mathcal{N}$ represents a nonlinear operator, and $g(x)$ is a given continuous function. The NIM framework constructs a rapidly convergent iterative sequence $\{u_n\}_{n=0}^{\infty}$ whose limit approximates the exact solution. The convergence behavior and numerical performan... More >