Applied Mathematics Commons^™

Bifurcation Exploration Of Ion Acoustic Solitons Formation Of A Nonlinear Beta Fractional Kadomtsev-Petviashvili Burger Model In Plasma State, Mst. Razia Pervin, Alrazi Abdeljabbar, Fahad Sameer Alshammari, Mst. Shekha Khatun, Harun Or-Roshid

Mathematical Modelling and Numerical Simulation with Applications

This research presents an extensive investigation of Ion acoustic soliton dynamics governed by a Beta-fractional Kadomtsev-Petviashvili-Burgurs (KPB) model. By engaging the planar dynamical system scheme in aggregation with the extended $(\phi, \psi)$ expansion, Kudryashov expansion, and the NMKM analytic schemes, we create a broad class of exact nonlinear pattern wave solutions. The local stability edifice of the fractional plasma model is explored through bifurcation theory, enabling the far-reaching classification of all admissible phase diagrams. Conforming Ion acoustic wave structures allied with every detour alignment are systematically assembled. Owing to the fractional and dissipative appearances of the model, an all-embracing assortment …

Employing Effective Solution Methods For Caputo-Based Sequential Fractional Models, Eman A. A. Ziada, Mohamed F. Abouelenein, Hijaz Ahmad, Monica Botros

Mathematical Modelling and Numerical Simulation with Applications

This paper investigates a class of nonlinear sequential singular fractional differential equations (FDEs) involving Caputo derivatives. This type of equation has several key advantages that enhance its value, such as capturing memory and hereditary effects. Viscoelastic materials and anomalous diffusion, as well as biological systems, can take advantage of this feature. In addition, fractional derivatives possess a sequential structure that enables the implementation of multiscale processes and hierarchical memory responses. Moreover, it provides an effective and flexible framework for solving differential equations compared to classical differential equations. It can therefore be used to model complex systems in physics, biology, and …

Numerical Simulations And Hyers-Ulam Stability Of A Novel Nonlocal Anthropogenic Cutaneous Leishmaniasis Mathematical Model, Khalid Fanoukh Al Oweidi, Zakirullah -, Kamal Shah, Thabet Abdeljawad

Mathematical Modelling and Numerical Simulation with Applications

In this work, the fractal-fractional Atangana-Baleanu derivative with the Mittag-Leffler kernel is employed to capture the memory and hereditary effects inherent to anthropogenic cutaneous leishmaniasis transmission dynamics. The Banach fixed-point theorem and contraction mapping principle are used to prove the existence and uniqueness of solutions, while Hyers-Ulam stability of the system is analyzed to demonstrate the robustness of solutions with respect to small perturbations. Using a nonlinear least-squares approach, model parameters and fractional order are estimated using epidemiological data from the World Health Organization. The basic reproduction number $R_0 = 0.53$ indicates that the disease is under control after adding …

Markov-Modulated Queueing Network For Mobile Traffic Aggregation With Threshold-Controlled Buffers, Anton A. Esin, Elmira Yu. Kalimulina

Mathematical Modelling and Numerical Simulation with Applications

We study the problem of data transmission from mobile platforms operating in high-speed transit between cellular base stations, under conditions of unstable and intermittent connectivity. Conventional queueing and connectivity models often fail to capture the combined effects of rapidly changing signal conditions, finite buffer capacity, and dynamic topology. We aim to develop a tractable yet expressive model that integrates stochastic link availability, queue dynamics, and buffer control. We propose a mathematical framework based on queues whose service intensities are modulated by a continuous-time Markov chain (CTMC) representing signal conditions along a high-speed trajectory. The core subsystem is a two-stage (aggregation …

Exact Soliton Solutions Of The Nonlinear Time-Fractional Schrödinger Equation Via Atangana–Baleanu And M-Truncated Operators, Bahadır Kopçasiz, Fatma Nur Kaya Sağlam, Mehmet Şenol

Mathematical Modelling and Numerical Simulation with Applications

The main objective of this work is to obtain exact soliton solutions for a nonlinear time-fractional equation model describing wave profiles arising in various physical systems. To derive different wave structures associated with the considered model, two analytical techniques are employed: the extended G'\G^2-expansion method and the modified auxiliary equation (MAE) approach. A wave transformation is applied to reduce the nonlinear time-fractional equation to a nonlinear ordinary differential equation (NLODE) by means of the M-truncated and Atangana-Baleanu (AB) fractional operators. Several classes of solutions, including exponential, hyperbolic, and trigonometric wave forms, are obtained. Over and above the analytical results, graphical …

Dynamical Analysis And Optimal Control Of The Mpox Transmission Model With Stratified Susceptibility, Tuhfatul Janan, Fatmawati Fatmawati, Cicik Alfiniyah, Santi Martini, Dipo Aldila, Agus Hasan

Mathematical Modelling and Numerical Simulation with Applications

This study develops a mathematical model of Mpox transmission that combines stratified susceptibility (low-risk and high-risk groups) with vaccinated and asymptomatically infected compartments. The analysis of the model begins with examining the well-posedness, boundedness, and nonnegativity conditions for the solutions. The local stabilities of the equilibria are examined through the Jacobian matrix and phase plane analysis, while the global stabilities are provided through Lyapunov functions. The estimated parameters are verified using epidemiological data on Mpox cases in the United States, with an MAPE of 2.20% and R_0 > 1, indicating that Mpox remains endemic. Sensitivity analysis indicates that the contact rate …

Patterns Of Multimorbidity Among Low-Income Adults Who Smoke With Implications For Tailored Interventions: A Cluster Analysis Using A Mixture Of Bernoulli Model, Monique T. Cano, Michael R. Lindstrom, Oscar F. Rojas Perez, Ricardo F. Muñoz

School of Mathematical & Statistical Sciences Faculty Publications

Introduction: Smoking cigarettes remains a leading modifiable risk factor for preventable health conditions. In the United States, the health burden of smoking disproportionately impacts low-income individuals. Multimorbidity is common in this group, complicating treatment and worsening outcomes. Identifying multimorbidity clusters can support targeted, individualized interventions. This study aimed to identify multimorbidity clusters among individuals who smoke and experience economic hardship and provide clinical recommendations to enhance health outcomes.

Method: Individuals who smoke and experience economic hardship (N = 60) were recruited from the San Francisco Health Network (SFHN) and were assessed for physical and mental conditions. Cluster analysis was …

(Si16-04) Some Fixed Point Theorems On Chatterjea Type Contractions, Irom Shashikanta Singh, Y. Mahendra Singh

Applications and Applied Mathematics: An International Journal (AAM)

This paper establishes the existence of fixed points related to strict Chatterjee contractive mappings by relaxing the compactness of the underlying spaces and the continuity of the mapping involved, using altering distance functions and comparison functions in the general setting of metric spaces. Several non-trivial and illustrative examples are provided to demonstrate, support, and validate the obtained theoretical results. In addition, a theorem that can characterize the completeness of metric spaces through the existence of fixed points is rigorously proven and discussed. Furthermore, a theorem on strict Chatterjea-type modulus contractive mappings without continuity assumptions and with relaxed compactness conditions is …

An Odd Protocol For An Agent-Based Model Of Hepatitis C Virus Transmission In A Homogeneous Syringe-Sharing Network, Seun Ale, Que Thi Nguyet Nguyen Dr., John D. Kelleher Prof., Elizabeth Hunter Dr.

Reports

The model described in this ODD is an agent-based model of hepatitis C virus (HCV) transmission among people who inject drugs (PWID). The model assumes homogeneous mixing among syringe-sharing agents, without any form of heterogeneity in the agents interactions or syringe-sharing attitude. All syringe-sharing PWID are treated as identical in terms of their interaction frequency and syringe-sharing probability. Interactions are generated dynamically using proximity-based sampling at each timestep (one day), allowing agents to form syringe-sharing interactions based on spatial closeness. The number of daily interaction events is fixed at the population level, and each syringe-sharing agent has the same probability …

An Odd Protocol For An Agent-Based Model Of Hepatitis C Virus Transmission With Inter- And Intra-Group Structural And Behavioural Heterogeneous Syringe-Sharing Networks (5), Seun Ale, Que Nguyen Dr., John D. Kelleher Prof., Elizabeth Hunter Dr.

Reports

The model described in this ODD is an agent-based model of hepatitis C virus (HCV) transmission among people who inject drugs (PWID). The model incorporates structural heterogeneity through a three-group interaction framework and behavioural heterogeneity through group-specific syringe-sharing rates with additional intra-group variability. The syringe-sharing population in the model is divided into core, inner, and outer circle groups representing individuals with high, moderate, and low levels of syringe-sharing interaction intensity, respectively. In addition to differences in the number of daily interaction opportunities across groups, agents in each group are assigned syringe-sharing probabilities that vary at the individual level around their …

An Odd Protocol For An Agent-Based Model Of Hepatitis C Virus Transmission In A Two-Group Structural Heterogeneous Syringe-Sharing Network (M2), Seun Ale, Que Nguyen Dr., John D. Kelleher Prof., Elizabeth Hunter Dr.

Reports

The model described in this ODD is an agent-based model of hepatitis C virus (HCV) transmission among people who inject drugs (PWID). The model extended a baseline homogeneous model by incorporating structural heterogeneity via a two-group interaction framework. The syringe-sharing population in the model is divided into inner and outer circle groups representing individuals with differing levels of syringe-sharing interaction intensity. While all agents share the same syringe-sharing probability and epidemiological processes remain identical across agents, the number of daily interaction opportunities differs between the two groups. Interactions in the model are generated dynamically using proximity-based sampling at each timestep …

An Odd Protocol For An Agent-Based Model Of Hepatitis C Virus Transmission In A Three-Group Structural Heterogeneous Syringe-Sharing Network (M3), Seun Ale, Que Nguyen Dr., John D. Kelleher Prof., Elizabeth Hunter Dr.

Reports

The model described in this ODD is an agent-based model of hepatitis C virus (HCV) transmission among people who inject drugs (PWID). The model incorporates structural heterogeneity through a three-group interaction framework. The syringe-sharing population in the model is divided into core, inner, and outer circle groups representing individuals with high, moderate, and low levels of syringe-sharing interaction intensity, respectively. While the syringe-sharing rate and all epidemiological processes remain identical across agents, the number of daily interaction opportunities differs by agent grouping, capturing variation in structural position within the syringe-sharing network. Interactions are generated dynamically using proximity-based sampling at each …

An Odd Protocol For An Agent-Based Model Of Hepatitis C Virus Transmission With Inter-Group Structural And Behavioural Heterogeneous Syringe-Sharing Networks (M4), Seun Ale, Que Nguyen Dr., John D. Kelleher Prof., Elizabeth Hunter Dr.

Reports

The model described in this ODD is an agent-based model of hepatitis C virus (HCV) transmission among people who inject drugs (PWID). The model incorporates structural heterogeneity through a three-group interaction framework and behavioural heterogeneity through group-specific syringe-sharing rates. The syringe-sharing population in the model is divided into core, inner, and outer circle groups representing individuals with high, moderate, and low levels of syringe-sharing interaction intensity, respectively. In addition to differences in the number of daily interaction opportunities across groups, agents in each group are assigned distinct syringe-sharing probabilities, reflecting variation in risk-taking behaviour across structural groups within the syringe-sharing …

Assessing The Geomechanical Modelling Of Underground Reservoir For Co₂ Storage Trapping Mechanisms, Bonavian Hasiholan, Mohammed Ali Farea, Elhassan Mostafa Abdallah, Sami Abdelrahman M. Yagoub, Yasir Mukhtar

Mathematical Modelling and Numerical Simulation with Applications

Effective carbon dioxide (CO₂) storage is essential for mitigating climate change amid increasing global greenhouse gas emissions. This study investigates the influence of geomechanics on CO₂ storage performance within carbon capture and storage (CCS), focusing on structural, residual, and solubility trapping mechanisms using a fully coupled modeling framework. Two numerical models, with and without geomechanical effects, are developed to evaluate impacts on reservoir behavior, CO₂ migration, and trapping efficiency. Each mechanism is analyzed separately and within an integrated framework to assess their combined contributions. Results indicate that geomechanical coupling increases reservoir pressure, reduces CO₂ flow velocity, enhances migration control, and …

A Coupled Fractional Thermistor System Demonstrating Existence, Uniqueness, And Simulation Results With Two-Point Boundary Conditions, Yahia Awad, Angela Khattar, Hussein Fakih, Sami Hammoud, Karim Amin

Mathematical Modelling and Numerical Simulation with Applications

This paper studies a coupled system of Caputo fractional differential equations of orders $\alpha, \beta\in(1,2]$, subject to two-point boundary conditions. The model incorporates nonlinear nonlocal integral terms that capture the memory-dependent interactions between thermal and electrical dynamics in thermistor materials. We rigorously establish existence via Schaefer’s fixed-point theorem and uniqueness through Banach’s contraction principle in a Banach space of continuous and continuously differentiable functions. Additionally, we analyze Ulam–Hyers stability to quantify solution sensitivity to initial perturbations. A numerical example highlights the effects of fractional orders and nonlocal feedback on system behavior. This work generalizes classical thermistor models and provides a …

On Cartan’S Examples Of Isoparametric Hypersurfaces And Their Focal Submanifolds, Thomas E. Cecil, Patrick J. Ryan

Mathematics and Computer Science Department Faculty Scholarship

This paper is a survey of Cartan’s examples of isoparametric hypersurfaces in spheres and their focal submanifolds that were described in his fundamental work on the subject, which appeared in four papers [2]–[5] published during the period 1938–1940.

The Butterfly Effect In Economics: Exploring Chaos With A Simple Financial Model, Sandy Hs Herho

CODEE Journal

Wild swings in financial markets need not result from external shocks like earthquakes or wars—they can emerge from deterministic chaos. This article introduces kalimusada, an open-source Python library that lets students and instructors explore this phenomenon through a simple three- equation model of financial dynamics. The model couples interest rates, investment, and prices through nonlinear feedback, generating bounded but unpredictable oscillations characteristic of chaos. Tiny differences in starting conditions—smaller than any measurement could detect—grow exponentially until two initially identical economies follow completely different paths. The library provides ready-to-use tools for visualizing this “butterfly effect” in economics, computing divergence metrics, and …

Systematic Synthesis Of Crispr/Cas Applications For Enhancing Salt Tolerance In Crops: A Decade Of Progress And Challenges, Xindi Sun, Fusheng Wu, Zhuanzhuan Ma, Guohao Liang, Shumei Chen, Xutong Hu, Shugao Fan, Ying Zhao

School of Mathematical & Statistical Sciences Faculty Publications

Soil salinity is a major constraint on global crop productivity, driving the need for salt-tolerant varieties. While CRISPR-Cas genome editing offers targeted solutions for trait improvement, significant biological and technical bottlenecks limit its application in conferring salt stress resilience. This systematic summarizes findings from 83 peer-reviewed studies (2015–2024) employing CRISPR/Cas technologies to improve salt tolerance in five major crops (rice, wheat, maize, sorghum, barley). Our systematic review reveals that early single-gene edits achieved modest gains (30–50% Na⁺ exclusion) but often showed limited yield gains in field settings, potentially due to compensatory regulation and environmental variation. The literature suggests that multiplex …

Making Mathematical Art Via The Harmonic And Perturbed Harmonic Functions, Mehmet Pakdemirli

Journal of Humanistic Mathematics

Starting from the definition of a harmonic function series, we define a new series which we call the perturbed harmonic function series. We explore the relationship of the new series with the Weierstrass and Riemann fractal functions as well as its convergence and differentiability properties. We then illustrate the potential of the harmonic functions in generating complex figures that sometimes resemble natural objects, with explicit numerical examples.

Gold And Silver In Balance: Khayyam’S Mathematical Analysis Of Binary Alloys, Yousef Yassi, Reza Yassi

Journal of Humanistic Mathematics

The history of titration dates back to Archimedes who established that an object submerged in a liquid displaces an amount of liquid whose weight is equal to the buoyant force acting on the object. Since then, many scientists and engineers have tried to optimize his approach or devise new instruments for titration purposes. Omar Khayyam (1048–1123), in addition to designing a hydro-static balance, developed mathematical approaches for titration of binary alloys, that is, alloys made up of only two elements. Here we explore the different versions of Khayyam’s work on titration given by various sources. We also compare the accuracy …