Faculty in the University of Dayton Department of Mathematics examine the art, science, application and philosophy of mathematics. Here, you can see a sampling of their research.

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Submissions from 2019

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Investigation of the Effect of Vehicle Color on Safety, Deogratias Eustace, Fayez Khalaf Alanazi, and Peter W. Hovey

Submissions from 2018

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Initial value problems for Caputo fractional differential equations, Paul W. Eloe and Tyler Masthay

Submissions from 2017

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Positive solutions of boundary value problems for ordinary differential equations with dependence on higher order derivatives, Ahlam Abid and Paul Eloe

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Eigenstate–Specific Temperatures in Two–Level Paramagnetic Spin Lattices, Mark Masthay, Calley N. Eads, Amber N. Johnson, R. Gerald Keil, Phillip Miller, Ross E. Jones, Joe D. Mashburn, and Harry B. Fannin

Submissions from 2016

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Almost Automorphic Solutions of Delayed Neutral Dynamic Systems on Hybrid Domains, Murat Adıvar, Halis Can Koyuncuoğlu, and Youssef Raffoul

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Optimal Control Analysis of Ebola Disease with Control Strategies of Quarantine and Vaccination, Muhammad Dure Ahmad, Muhammad Usman, Adnan Khan, and Mudassar Imran

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Upper and Lower Solution Method for Boundary Value Problems at Resonance, Samerah Al Mosa and Paul W. Eloe (0000-0002-6590-9931)

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Positive Solutions for a Singular Fourth Order Nonlocal Boundary Value Problem, John M. Davis, Paul W. Eloe (0000-0002-6590-9931), John R. Graef, and Johnny Henderson

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Nonlinear Interpolation and Boundary Value Problems, Paul W. Eloe (0000-0002-6590-9931) and Johnny Henderson

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Convolutions and Green’s Functions for Two Families of Boundary Value Problems for Fractional Differential Equations, Paul W. Eloe (0000-0002-6590-9931) and Jeffrey T. Neugebauer

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Smallest Eigenvalues for a Right Focal Boundary Value Problem, Paul W. Eloe (0000-0002-6590-9931) and Jeffrey T. Neugebauer

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Modeling Factors Contributing to Injury and Fatality of Run-off-Road Crashes in Ohio, Deogratias Eustace, Omar Eid Almutairi, and Peter W. Hovey

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Asymptotically Periodic Solutions of Volterra Integral Equations, Muhammad Islam

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Existence of Periodic Solutions for a Quantum Volterra Equation, Muhammad Islam and Jeffrey T. Neugebauer

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Integration Over Curves and Surfaces Defined by the Closest Point Mapping, Catherine Kublik and Richard Tsai

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Sphere Representations, Stacked Polytopes, and the Colin de Verdière Number of a Graph, Lon Mitchell and Lynne Yengulalp

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Identification of Control Targets in Boolean Molecular Network Models via Computational Algebra, David Murrugarra, Alan Veliz-Cuba, Boris Aguilar, and Reinhard Laubenbacher

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Necessary and Sufficient Conditions for Stability of Volterra Integro-dynamic Equation Systems on Time Scales, Youssef Raffoul

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Uniform Stability In Nonlinear Infinite Delay Volterra Integro-differential Equations Using Lyapunov Functionals, Youssef Raffoul and Habib Rai

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Theorems on Boundedness of Solutions to Stochastic Delay Differential Equations, Youssef Raffoul and Dan Ren

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Effects of Cell Cycle Noise on Excitable Gene Circuits, Alan Veliz-Cuba, Chinmaya Gupta, Matthew R. Bennett, Krešimir Josić, and William Ott

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Stochastic Models of Evidence Accumulation in Changing Environments, Alan Veliz-Cuba, Zachary P. Kilpatrick, and Krešimir Josić

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Coding Strategies, the Choquet Game and Domain Representability, Lynne Yengulalp

Submissions from 2015

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Fixed points and solutions of boundary value problems at resonance, Alaa Almansour and Paul W. Eloe

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Multi-term linear fractional nabla difference equations with constant coefficients, Paul W. Eloe and Zi Ouyang

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From Subcompact to Domain Representable, William Fleissner and Lynne Yengulalp

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Bounded, Asymptotically Stable, and L^1 Solutions of Caputo Fractional Differential Equations, Muhammad Islam

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Qualitative Theory of Functional Differential and Integral Equations, Muhammad Islam, Cemil Tunc, Mouffak Benchohra, Bingwen Lui, and Samir H. Saker

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Sobriety in Delta not Sober, Joe Mashburn

Submissions from 2014

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Conjugate points for fractional differential equations, Paul W. Eloe and Jeffrey T. Neugebauer

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Existence and comparison of smallest eigenvalues for a fractional boundary-value problem, Paul W. Eloe and Jeffrey T. Neugebauer

Periodic and Asymptotically Periodic Solutions in Coupled Nonlinear Systems of Volterra Integro-differential Equations, Muhammad Islam and Youssef Raffoul

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Modified Homotopy Perturbation Transform Method: A Paradigm for Nonlinear Boundary Layer Problems, Yasir Khan and Muhammad Usman

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Lyapunov Functionals that Lead to Exponential Stability and Instability in Finite Delay Volterra Difference Equations, Catherine Kublik and Youssef Raffoul

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A Generalization of Poincaré-Cartan Integral Invariants of a Nonlinear Nonholonomic Dynamical System, Muhammad Usman and M. Imran

Submissions from 2013

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Concavity of solutions of a 2n-th order problem with symmetry, Abdulmalik Altwaty and Paul W. Eloe

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An example employing convexity in functional fixed point arguments, Richard I. Avery, Paul W. Eloe, and Johnny Henderson

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Every Scattered Space is Subcompact, William Fleissner, Vladimir Tkachuk, and Lynne Yengulalp

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When Cp(X) is Domain Representable, William Fleissner and Lynne Yengulalp

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The Impact of Group Music Therapy on Negative Affect of People with Co-Occurring Substance Use Disorders and Mental Illnesses, Susan Gardstrom, Jacklyn Bartkowski, Joy Willenbrink, and Wiebke S. Diestelkamp

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Three Fixed Point Theorems: Periodic Solutions of a Volterra Type Integral Equation with Infinite Heredity, Muhammad Islam

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The Effects of Variable Viscosity on the Peristaltic Flow of Non-Newtonian Fluid through a Porous Medium in an Inclined Channel with Slip Boundary Conditions, Ambreen Afsar Khan, R. Ellahi, and Muhammad Usman

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An Implicit Interface Boundary Integral Method for Poisson’s Equation on Arbitrary Domains, Catherine Kublik, Nicolay M. Tanushev, and Richard Tsai

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A Spectral Order for Infinite Dimensional Quantum Spaces, Joe Mashburn

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Existence and uniqueness of solutions for impulsive fractional differential equations, Mujeeb ur Rehman and Paul W. Eloe

Submissions from 2012

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The role of concavity in applications of Avery type fixed point theorems to higher order differential equations, Abdulmalik A. Altwaty and Paul W. Eloe

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Gronwall's inequality on discrete fractional calculus, Ferhan M. Atici and Paul W. Eloe

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A Leggett-Williams type theorem applied to a fourth order problem, Richard Avery, Paul Eloe, and Johnny Henderson

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Existence and uniqueness conditions for a class of (k+4j)-point n-th order boundary value problems, Paul W. Eloe, Johnny Henderson, and Rahmat Ali Khan

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Uniqueness implies existence and uniqueness conditions for a class of (k+j)- point boundary value problems for n-th order differential equations, Paul W. Eloe, Johnny Henderson, and Rahmat Ali Khan

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Bounded Solutions of Almost Linear Volterra Equations, Muhammad Islam and Youssef Raffoul

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A study of the GAM approach to solve laminar boundary layer equations in the presence of a wedge, Rahmat Ali Khan and Muhammad Usman

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Eventual Periodicity of Forced Oscillations of Korteweg-de Vries Type Equation, Rahmat Ali Khan and Muhammad Usman

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A Meshless Numerical Solution of the Family of Generalized Fifth-order Korteweg-de Vries Equations, Syed Tauseef Mohyud-Din, Elham Negahdary, and Muhammad Usman

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Bifurcations in Steady State Solutions of a Class of Nonlinear Dispersive Wave Equation, Muhammad Usman and Paul W. Eloe (0000-0002-6590-9931)

Submissions from 2011

Existence of positive solutions to a singular system of boundary value problems, Naseer Ahmad Asif, Rahmat Ali Khan, and Paul W. Eloe

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Linear systems of fractional nabla difference equations, Ferhan M. Atici and Paul W. Eloe

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Two-point boundary value problems for finite fractional difference equations, Ferhan M. Atici and Paul W. Eloe

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Research in Mathematics Educational Technology: Current Trends and Future Demands, Shannon O. Driskell, Robert N. Ronau, Christopher R. Rakes, Sarah B. Bush, Margaret L. Niess, and David K. Pugalee

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Fully Nonlinear Boundary Value Problems with Impulse, Paul Eloe (0000-0002-6590-9931) and Muhammad Usman

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Optimal intervals for uniqueness of solutions for nonlocal boundary value problems, Paul W. Eloe and Johnny Henderson

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Uniqueness implies existence and uniqueness conditions for a class of (k+j)-point boundary value problems for nth order differential equations, Paul W. Eloe and Johnny Henderson

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Upper and lower solutions for regime-switching diffusions with applications in financial mathematics, Paul W. Eloe and R. H. Liu

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Non-Normality Points of β X\X, William Fleissner and Lynne Yengulalp

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Algorithms for Area Preserving Flows, Catherine Kublik, Selim Esedoglu, and Jeffrey A. Fessler

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Prospective Teachers' Use of Representations in Solving Statistical Tasks with Dynamic Statistical Software, Hollylynne Lee, Shannon O. Driskell, Suzanne R. Harper, Keith R. Leatham, Gladis Kersaint, and Robin L. Angotti

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Positive solutions of nonlocal boundary value problem for higher order fractional differential system, Mujeeb Ur Rehman, Rahmat Ali Khan, and Paul W. Eloe

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Global Well-posedness and Asymptotic Behavior of a Class of Initial-boundary-value Problems of the KdV Equation on a Finite Domain, Ivonne Rivas, Muhammad Usman, and Bingyu Zhang

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A New Undergraduate Curriculum on Mathematical Biology at University of Dayton, Muhammad Usman and Amit Singh

Submissions from 2010

A nonlocal boundary value problem for a nonlinear fractional differential equation with two indices, Bashir Ahmad and Paul Eloe

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Positive solutions for a system of singular second order nonlocal boundary value problems, Naseer Ahmad Asif, Paul W. Eloe, and Rahmat Ali Khan

Uniqueness conditions for a class of nonlocal boundary value problems, Paul W. Eloe and Rahmat Ali Khan

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Periodic Solutions of Neutral Delay Integral Equations of Advanced Type, Muhammad Islam, Nasrin Sultana, and James Booth

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Coarsening in High Order, Discrete, Ill-Posed Diffusion Equations, Catherine Kublik

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Linearly Ordered Topological Spaces and Weak Domain Representability, Joe Mashburn

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Coarser Connected Metrizable Topologies, Lynne Yengulalp

Submissions from 2009

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Discrete fractional calculus with the nabla operator, Ferhan M. Atici and Paul W. Eloe

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Initial value problems in discrete fractional calculus, Ferhan M. Atici and Paul W. Eloe

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Preface [Honoring the career of John Graef on the occasion of his sixty-seventh birthday], Paul W. Eloe and Johnny Henderson

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Double barrier option under regime-switching exponential mean-reverting process, Paul W. Eloe, R. H. Liu, and J. Y. Sun

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Forced Oscillations of the Korteweg-de Vries Equation on a Bounded Domain and their Stability, Muhammad Usman and Bingyu Zhang

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Coarser Connected Topologies and Non-Normality Points, Lynne Yengulalp

Submissions from 2008

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Optimal selling rules in a regime-switching exponential Gaussian diffusion model, Paul W. Eloe, R. H. Liu, and Masako Yatsuki

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Qualitative Properties of Nonlinear Volterra Integral Equations, Muhammad Islam and Jeffrey T. Neugebauer

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An Order Model for Infinite Classical States, Joe Mashburn

Submissions from 2007

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A transform method in discrete fractional calculus, Ferhan M. Atici and Paul W. Eloe

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Fractional q-calculus on a time scale, Ferhan M. Atici and Paul W. Eloe

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Uniqueness implies existence and uniqueness conditions for nonlocal boundary value problems for nth order differential equations, Paul W. Eloe and Johnny Henderson

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Periodic Solutions of Neutral Nonlinear Systems of Differential Equations with Functional Delay, Muhammad Islam and Youssef Raffoul

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A Comparison of Three Topologies on Ordered Sets, Joe Mashburn

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A Spectral Order for Infinite Dimensional Quantum Spaces: A Preliminary Report, Joe Mashburn

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Forced Oscillations of a Class of Nonlinear Dispersive Wave Equations and their Stability, Muhammad Usman and Bingyu Zhang

Submissions from 2006

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A qualitative analysis on nonconstant graininess of the adaptive grids via time scales, Paul W. Eloe, Stefan Hilger, and Qin Sheng

Multiple solutions of a boundary value problem on an unbounded domain, Paul W. Eloe, Eric R. Kaufmann, and Christopher C. Tisdell

Submissions from 2005

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Positive operators and maximum principles for ordinary differential equations, Paul W. Eloe

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Positive solutions of a nonlinear nth order boundary value problem with nonlocal conditions, Paul W. Eloe and Bashir Ahmad

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Existence, uniqueness and constructive results for delay differential equations, Paul W. Eloe, Youssef N. Raffoul, and Christopher C. Tisdell

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Stability Properties of Linear Volterra Integrodifferential Equations with Nonlinear Perturbation, Muhammad Islam and Youssef Raffoul

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Boundedness and Stability in Nonlinear Delay Difference Equations Employing Fixed Point Theory, Muhammad Islam and Ernest Yankson

Submissions from 2004

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Maximum principles for a family of nonlocal boundary value problems, Paul W. Eloe