Research Interests

From concrete to abstract, and from abstract to concrete, I am interested in the study of nonlinear operator equations, solutions and positive solutions for nonlinear differential and difference equations, fixed point theory, machine learning and deep neural networks. I have developed new spectral theory for nonlinear operators, semilinear operators, and new theorems on fixed-point index that have been applied to existence of positive solutions for ODE (Ordinary Differential Equations), PDE (Partial Differential Equations), FDE (Fractional-order Differential Equations) and their discrete counterparts in the form of difference equations.

At the mean time, I have ongoing projects on machine learning algorithms using deep neural network with applications in data analytics. Mathematical and computational modelling techniques have been applied to the study of bike sharing, recommendation systems, image recognition, energy efficiency, cost reduction and other applications.

Courses

• Database Management Systems, COIS 3400H, Fall 2023
• Modelling and Simulation, COIS 4470H, Winter 2024

Current Graduate Students

• Co-supervisor, Ph.D candidate at the School of Computing, Queen’s University
• Supervisor, M.Sc. candidate at the AMOD (Applied Modelling and Quantitative Method) graduate program, Trent University
• Co-supervisor, M.Sc. candidate at the Department of Mathematics and Statistics, Memorial University of Newfoundland

Conferences

• Co-organizer, Differential, Difference and Integral Equations, Techniques and Applications, Special Session (SS109) at the 14th AIMS Conference on Dynamical Systems, Differential Equations and Applications, December 16-20, 2024, Abu Dhabi, UAE
• Main speaker, Functional Analysis: Methods and Applications (FAMA 2024), On the occasion of retirement of Professor Giuseppe Marino, Amantea and Renee (Cosenza), 6-8 June 2024.
• Conference Chair, the 33rd International Conference on Software Engineering and Data Engineering, October 21-22, 2024, San Diego, CA, US
• IEEE/ICIS 2023, Co-organizer for the Special Session Quantitative Modeling and Analysis: Theoretical and Empirical Approaches.
• Invited talks, the 13th AIMS Conference on Dynamical Systems, Differential Equations and Applications, May 31–June 4th, 2023 Wilmington, NC, USA.
• Invited talk, Conference in Memory of Professor Andrzej Granas – Topological Methods in Nonlinear Analysis: Recent Advances, Centre de Recherches Mathématiques (CRM), Montreal, Canada, July 2022.

Editorial Activities

• Guest Editor, Fractal and Fractional, Special Issue “Boundary Value Problems for Nonlinear Differential Equations: Theory, Method and Application”, deadline for manuscript submission: 31, January 2024
• Co-editor, Special Issue on Recent Advances In Neural Network Methods for PDE and its Application, Journal of Mathematical Methods in the Applied Sciences, August 2020.

Supports from NSERC and MITACS are greatly acknowledged

• NSERC Individual Discovery Grant, 2023–2029
• NSERC Individual Discovery Grant, 2021
• NSERC Engage Plus Grant, 2021
• NSERC Engage Grant, 2018–2019
• NSERC Individual Discovery Grant, 2016–2020
• MITACS Accelerate Internship Award, 2015
• MITACS Accelerate Internship Award, 2014
• Connect Canada Internship Award, 2014
• MITACS Accelerate Internship Award, 2013
• Canadian Bureau for International Education, Canadian-Brazil Ciencia sem Fronteiras, 2013.
• MITACS Accelerate Internship Award, 2012
• NSERC Individual Discovery Grant, 2011–2015
• NSERC Individual Discovery Grant, 2005–2009
• NSERC Individual Discovery Grant, 2001–2004

Recent Publications

• Integral operators in b-matric and generalized b-metric spaces and boundary value problems, Fractal Fract. 2024, 8(11), 674: https://doi.org/10.3390/fractalfract8110674. (co-author: C. Middlebrook).
• Dynamic behavior of a stochastic tungiasis model for public health education. Discrete Dyn. Nat Soc. 2022: 1-13. (co-authors: L. Kong, L. Li, S. Kang, Y. Liu).
• Positive solutions for a class of integral boundary value problem of fractional q-difference equations. Symmetry 2022, 14(11), 2465. https://doi.org/10.3390/sym14112465, 11 pages. (co-authors: S. Kang, Y. Zhang, H. Chen).
• Recent advances in neural network methods for FDE and its application. Math Meth Appl Sci. 2022: 1-3. (co-authors: F. Gao, X. Zhang, F. Ge).
• Estimating the energy forecasting uncertainty for reliable AI autonomous smart grid design, Energies 2021, 14, 247, 1–15. https://doi.org/10.3390/en14010247.(co-authors: M. Selim, R. Zhou, P. Quinsey).
• Nonlinear spectrum and fixed point index for a class of decomposable operators, Mathematics 2021, 9(3), 1–9. https://doi.org/10.3390/math9030278. (co-authors: S. Kang, Y. Zhang).
• Existence of solutions for a class of fractional difference equations at resonance, Stud Appl Math. 146(4), (2021), pp. 881–900. https://doi.org/10.1111/sapm.12368. (co-authors: H. Chen, Y. Cui, S. Kang, Y. Lu).
• Evaluation of parallel and sequential deep learning models for music subgenre classification. Math Fdn Comput. 4(2) (2021), 131–143. (co-author: M. Feng).

Opening Positions for Graduate Students (M.Sc./Ph.D)

– Machine Learning, Neural Networks, Differential Equations

My research team currently has openings for motivated graduate students (M.Sc. or Ph.D). The potential research projects are in the following areas:

1. Machine Learning and Neural Networks

This topic applies machine learning techniques, including deep learning with neural networks to data analytics in a particular application area. The objective is to study the efficiency of the learning algorithm and optimize the performance.

• Neural Network and Differential Equations

Modelling neural networks with differential/difference equations. Stability and convergence analysis on the algorithms from properties of the dynamical systems.

•  Solutions for Differential Equations – existence and stability

Applying both topological and numerical methods on the study of differential equations including existence, uniqueness and multiplicity of solutions for BVPs (Boundary Value Problems) and IVPs (Initial Value Problems).

Qualifications

• B.Sc. or M.Sc. in the fields of Mathematics, Computer Science or Electrical Engineering.
• Computer programming experience
• Strong background in mathematical analysis
• Previous research experience is a plus but not required

Funding available for qualified candidates.