Journal of Mathematical Analysis and Modeling

Approximate solutions to malaria transmission models with seasonality and awareness: A comparative analysis of ADM and HPM

Abimbola Abolarinwa, Isaac O Olusola — Tue, 27 Oct 2026 00:00:00 +0000

Mathematical modelling provides critical insights into malaria transmission dynamics and interven tion efficacy. While standard numerical solvers provide quantitative solutions, semi-analytical methods yield closed-form series approximations that enhance qualitative and parametric understanding. This study com paratively investigates two prominent semi-analytical techniques, the Adomian Decomposition Method (ADM) and the Homotopy Perturbation Method (HPM), applied to a seasonally-forced malaria transmission model. The underlying formulation encompasses human behavioral awareness, a structured mosquito life cycle, and seasonal forcing, resulting in a twelve-dimensional coupled non-autonomous nonlinear system. Explicit recur sive algorithms for ADM and HPM are derived and validated against fourth-fifth order Runge–Kutta numeri cal benchmarks using biologically realistic parameters. The comparative evaluation indicates compartment dependent performance: HPM exhibits high precision for human epidemiological classes over short intervals, while ADM demonstrates superior stability across mosquito developmental stages and awareness dynam ics over extended time periods. Numerical experiments further show that intensified awareness campaigns significantly curtail infection prevalence across both host and vector populations. The methods remain com putationally tractable for 12D systems. Our findings therefore provide practical guidance for selecting semi analytical schemes according to compartment and time-scale in high-dimensional epidemiological systems.

Analysis of a Fractional Predator–Prey System Incorporating Strong Allee Effects and Nonlinear Defensive Feedback

SARITA PIPPAL — Tue, 27 Oct 2026 00:00:00 +0000

This paper presents a fractional-order predator–prey model incorporating a strong Allee effect in the prey population and a nonlinear anti-predator feedback mechanism in the predator population. The model is formulated using the Caputo fractional derivative of order α (0 < α ⩽ 1), allowing the inclusion of memory and hereditary effects that are frequently observed in ecological systems. The prey population is assumed to experience a strong Allee effect, while predator dynamics are regulated through a density-dependent feedback response that reflects behavioural adaptation and defensive interactions. Fundamental mathematical proper ties of the model, including existence, uniqueness, positivity, and boundedness of solutions, are established to ensure biological feasibility. Equilibrium points of the system are determined, and their local stability is investigated through Jacobian linearization and eigenvalue analysis. For the fractional-order model, stabil ity conditions are examined using the fractional eigenvalue criterion, highlighting the influence of memory effects on the asymptotic behaviour of the system. To illustrate the theoretical findings, extensive numer ical simulations are performed using the fractional Adams–Bashforth–Moulton predictor–corrector scheme. Phase-plane analysis, equilibrium investigations, and two-parameter stability maps are employed to examine the influence of the carrying capacity, Allee threshold, interaction strength, feedback intensity, and fractional order on the system dynamics. The results demonstrate that increasing the carrying capacity enlarges the biologically feasible region and promotes persistence, whereas stronger Allee effects reduce the coexistence domain and increase the risk of extinction. Furthermore, the nonlinear anti-predator feedback significantly modifies predator survival and stability characteristics. A comparative study between the classical integer order model (α = 1) and the fractional-order formulation (0 < α < 1) reveals that ecological memory plays a stabilizing role. Fractional dynamics generate smoother trajectories, reduced oscillatory behaviour, and slower convergence toward equilibrium states when compared with the corresponding classical system. These memory-induced effects moderate abrupt population fluctuations and promote more realistic ecolog ical responses. Overall, the proposed model provides a flexible framework for understanding the combined roles of memory, Allee effects, and behavioural feedback in predator–prey interactions, offering new insights into the stability and persistence of ecological systems..

Stability Analysis and Approximation of Time Fractional Hyperbolic Integro Partial Differential Equations

Fatih ÖZBAĞ — Tue, 27 Oct 2026 00:00:00 +0000

This study investigates fractional order hyperbolic integro-differential equations involving Caputo fractional derivatives, emphasizing the need for accurate approximate solutions. To address this, first- and second-order finite-difference schemes are proposed for the associated initial boundary value problem. Detailed error analyses, presented through tables and figures, demonstrate the accuracy of the numerical results. Furthermore, Von Neumann stability analysis is carried out, highlighting its role in ensuring the reliability and consistency of the devel- oped schemes. Numerical experiments validate the effectiveness of the methods by confirming excellent agreement with exact solutions. Comparative evaluations across different fractional orders are performed using identical grid numbers, with illustrative plots showing behavior for large spatial and temporal vari- ables. The findings emphasize that finite-difference approaches, supported by stability analysis, offer a reliable and efficient framework for solving Caputo time- fractional hyperbolic integro-differential equations, underlining their applicability in broader fractional calculus and differential equation contexts.

An Improved Residual Power Series Method for Radiative MHD CuO-Water Nanofluid Convection in a Semi-Porous Stretching Channel

Muhammad Usman, Ghani Irfan, Muhammad Yousaf — Tue, 27 Oct 2026 00:00:00 +0000

This study considers radiative magnetohydrodynamic forced convection of a CuO–water nanofluid in a
semi-porous channel with a stretching wall, with Joule heating included in the energy equation. By applying
suitable similarity transformations, the governing continuity, momentum, and energy equations are reduced
to a coupled system of nonlinear ordinary differential equations. The resulting boundary value problem is
solved using the Improved Residual Power Series Method (IRPSM). The validity of the proposed approach
is confirmed through comparison with available benchmark results, showing close agreement. The effects
of the Reynolds number, Hartmann number, suction parameter, and nanoparticle shape on the velocity and
temperature distributions are examined. The results indicate that the magnetic field suppresses the flow,
suction significantly alters the thermal and momentum boundary layers, and platelet-shaped nanoparticles
yield the highest local Nusselt number among the considered shapes. The study demonstrates that IRPSM is
an effective and accurate semi-analytical tool for this class of nonlinear transport problems.

A Rebuttal to “Proper Definitions of Dirichlet Conditions and Convergence of Fourier Representations" by P. Singh et al.

AKHILESH KUMAR SINGH — Tue, 27 Oct 2026 00:00:00 +0000

In their lecture note [1], P. Singh et al. (2022) argue that the Dirichlet conditions (DCs) commonly
stated in engineering texts are incomplete, and propose bounded variation (BV) together with an “extended
Carleson–Hunt theorem” as a more appropriate framework. This paper re-examines these claims in light
of the historical development of Fourier convergence theory and the distinction between Fourier-series and
Fourier-transform settings. The standard textbook conditions—absolute integrability, finitely many extrema,
and finitely many finite discontinuities—are shown to be a faithful modern formulation of classical Dirichlet
type sufficient conditions for Fourier-series convergence on a finite period. Bounded variation, introduced by
Jordan (1881), constitutes a later and strictly broader criterion rather than a correction of Dirichlet’s original
hypotheses. Moreover, while BV(T) ⊂ Lp(T) holds on any finite period, BV(R) ̸⊂ L1(R); consequently
BV alone does not guarantee the existence of the classical Fourier transform on the real line. Re-analysis
of the seven examples in [1] confirms that they do not expose any deficiency in the classical Dirichlet-type
conditions, but rather illustrate the need to distinguish domains, function spaces, and modes of convergence.
No replacement of the standard Dirichlet-type conditions is required for Fourier-series convergence on a finite
periodic domain.

Unique Common Fixed Point Theorem for a Sequence of Mappings

Hakima Bouhadjera — Tue, 27 Oct 2026 00:00:00 +0000

In this paper, a unique common fixed point result for four mappings, two by two occasionally weakly
biased of type (A) in a metric space is obtained. Our reason behind this contribution is to investigate the
existence and uniqueness of common fixed points in the recent weaker framework of occasionally weakly
biased mappings of type (A). Moreover, a suitable example is furnished to highlight our main result. In
addition, from our principal theorem, we derived some results, and to generalize our fundamental theorem,
a unique common fixed point result of a sequence of mappings is presented.