Journal of Mathematical Analysis and Modeling

Novel Exact Solutions of a Higher-Dimensional Complex KdV System with Conformable Derivative Using the Generalized Expansion Method

Muhammad Ishfaq Khan, Usama Ali, Beenish — Fri, 12 Sep 2025 00:00:00 +0000

In this paper, we investigate the (2+1)-dimensional complex modified Korteweg-de Vries (CmKdV) system using the conformable derivative. The CmKdV system is a beneficial model in the field of nonlinear wave theory such as fluid flow, optical communication, and plasma physics. Explicit solutions are constructed, including periodic, solitary, and shock waves form using the Jacobi elliptic function expansion method. The solutions obtained are visually presented in various dimensions using Mathematica, providing a clear physical understanding of the effects of the conformable fractional derivative. This research enhances understanding of soliton behavior in complex nonlinear systems and demonstrates the effectiveness of combining conformable derivatives with analytical methods, while also providing new insights into the dynamics and diverse forms of propagating fluid waves.

Four-Point Hybrid Block Method for direct Solution of Third-Order Ordinary Differential Equations

Kayode S. J., Adebisi A. A. — Wed, 05 Nov 2025 00:00:00 +0000

This article presents a four-point hybrid block method for directly solving third-order ordinary differential equations. The method was derived by adopting interpolation and collocation techniques using the Chebyshev polynomial of the first kind as a basis function. The developed method was implemented in block mode. The fundamental properties of the method were investigated to confirm its usability. To evaluate its performance, the method was tested by solving linear and nonlinear initial value problems of third-order ordinary differential equations. The numerical results are compared with existing methods to determine their accuracy. The results show a better accuracy over the existing methods.

Modeling the Dynamics of Corruption and Optimal Control in Public Sectors

Odeli J. Kigodi, Mohamedi S. Manjenga, Fadhili M. Mrope, Honda N. Masasila — Wed, 05 Nov 2025 00:00:00 +0000

We introduce a Susceptible-Corrupted-Paying Well-Recovered (SCPwR) model specifically designed to analyze corruption dynamics within the public sector. This model is demonstrated to be well posed both epidemiologically and mathematically. Our results show that all model solutions remain positive and bounded given initial conditions within a meaningful set. We investigate the existence of unique corruption-free and endemic equilibrium points and calculate the basic reproduction number. The local and global stability of these equilibrium points is then analyzed. Our findings indicate that the system has a locally asymptotically stable corruption-free equilibrium when R_e < 1 and unstable when R_e > 1 . Additionally, the corruption endemic equilibrium point E^* is globally asymptotically stable only if dL/dt< 0 . Numerical implementation of the model suggests that corruption will persist in public sectors if civil servants are not adequately compensated.

Classical optimal single-step hybrid block techniques for ODEs: Combined basis functions with dynamic collocation strategy

O. V. Atabo, A. T. Cole, S. O. Adee, P. O. Olatunji , E. O. Omole, Q. O. Ahman — Wed, 05 Nov 2025 00:00:00 +0000

We introduce a new class of block methods based on a hybrid basis of Hermite probabilists’ polynomials and exponential polynomials. The proposed techniques exploit the complementary strengths of both families, offering enhanced accuracy, stability, and flexibility compared with schemes built on a single polynomial type. The methods employ interpolation and dynamic collocation and are formulated within a second-derivative framework. To strengthen their structure, additional terms are generated through the recurrence relation of Hermite probabilists’ polynomials, whose orthogonality provides further advantages over exponential functions. Since the accuracy of numerical methods depends largely on discretization constants, this hybridization, together with the clustered mesh points, help reduce discretization errors and error constants while maintaining stability. Rigorous theoretical analysis establishes A-stability and convergence of the schemes. Although their algebraic order of convergence is relatively low, numerical experiments demonstrate that the methods achieve improved accuracy and competitive precision factors compared with existing block approaches. These results suggest that hybrid polynomial bases provide a promising pathway for the development of robust and efficient block algorithms in numerical analysis.

A Mathematical Analysis of Tuberculosis Transmission Using a Two-Age Group Compartmental Model

Frankline Chidi Eze, Livinus Loko Iwa, Umar Muhammad Adam, Alogla Monday Audu — Wed, 05 Nov 2025 00:00:00 +0000

In this study, a two-age-group compartmental model for tuberculosis transmission is developed and an alyzed, distinguishing between individuals below 10 years and those above this age. The model includes key epidemiological features such as reinfection within both age groups and the transition of treated individuals back to full susceptibility, representing realistic post-treatment outcomes. Essential analytical properties like non-negativity, existence, and uniqueness of solutions are established to confirm the model’s biological validity. Equilibrium analysis identifies both disease-free and endemic steady states, and the basic reproduc tion number, R_0, is derived using the next-generation matrix method. Local stability analysis indicates that the disease-free equilibrium is asymptotically stable when R_0 < 1, suggesting effective disease control, while instability occurs when R_0 > 1, resulting in disease persistence. Additionally, the global stability of both equilibrium states is rigorously proven-employing the Metzler matrix method for the disease-free case and a Lyapunov function for the endemic state-demonstrating the model’s strong dynamical behavior. Sensitivity analysis of R_0 identifies parameters that significantly impact tuberculosis transmission dynamics, offering in sights for targeted intervention strategies. Scenario analyses, supported by three-dimensional plots, illustrate how variations in parameters influence R_0 and the spread of infection. Numerical simulations conducted in Python validate the analytical findings, indicating an increase in immunity as individuals age from under 10 to above 10 years, while higher contact rates among children considerably enhance transmission potential. This study provides a deeper understanding of age-dependent tuberculosis dynamics and offers relevant implications for disease control policies across different age groups.

Solvability of Generalized Fractional Hybrid Differential Inclusions in Banach Algebras

Tamer Nabil, T. M El-Adawy — Wed, 05 Nov 2025 00:00:00 +0000

This research paper study the solvability of hybrid fractional differential inclusions involving generalized Caputo fractional derivative with boundary conditions under certain conditions. The existence theorems are proved by using hybrid fixed–point approach in Banach algebras of Dhage, which he presented in 2006. An example, lastly, is proposed to check the efficiency of the above-mentioned theorems. The results are novel and provide extensions to some of the findings known in the literature.

Approximate Solutions of Bratu-Type Boundary Value Problems

Richard Olu Awonusika, Peter Oluwafemi Olatunji, Bunmi Segun Rotimi — Wed, 05 Nov 2025 00:00:00 +0000

The Bratu's equation is a strongly nonlinear second-order ordinary differential equation that arises in electrospinning process and models temperature distribution within a flame in combustion theory. Bratu-type equations are used to simulate the ignition of flammable gases and flame propagation. In this paper, two methods are proposed to obtain highly accurate and reliable approximate solutions of Bratu-type boundary value problems. The first technique is a power series method which is based on the generalised Cauchy product that simplifies the difficulty associated with the nonlinear terms. Subsequently, explicit recurrence relations for the expansion coefficients of the series solutions are obtained. The second approach uses a twelfth-order second derivative backward differentiation formula that is implemented as a boundary value method. This numerical method is referred to as second derivative backward differentiation boundary value method. Three examples are given to illustrate the effectiveness, reliability, and accuracy of the proposed methods. The results obtained from both methods are in excellent agreement with the known exact solution. Comparison of the approximate and exact solutions shows that the proposed methods are reliable and accurate in solving a class of strongly nonlinear boundary value problems of Bratu-type.