A Free Online Research Opportunity for Students & Scholars
ProfVista is pleased to announce the Summer Research Internship Program 2026, a fully free and online academic initiative designed to provide students, research scholars, and young learners with valuable research exposure under the guidance of experienced mentors from our faculty network.
This 45-day internship aims to help participants develop research skills, analytical thinking, technical writing abilities, and subject-specific knowledge through structured project work conducted remotely.
Program Highlights
✅ Completely Free of Cost
✅ Fully Online / Remote Mode
✅ Duration: 45 Days
✅ Guided by Experienced Faculty Mentors
✅ Flexible Working Schedule
✅ Research-Based Learning Experience
✅ Certificate upon Successful Completion
✅ Ideal for CV / Academic Profile Building
Who Can Apply?
Applications are invited from:
- Undergraduate Students
- Postgraduate Students
- Research Scholars
- Fresh Graduates
- Motivated Learners from Any Discipline
Students from Mathematics, Science, Engineering, Computer Science, Management, Humanities, and other backgrounds may apply depending on project availability.
Available Internship Projects
Project 1
Title: Mathematical analysis of a two-strain hepatitis B fractional-order model
Summary: The aim of this project is to analyze a two-strain hepatitis B model using modern tools from nonlinear dynamics and fractional calculus. The study will focus on determining the biological threshold and performing an asymptotic stability analysis of equilibrium points and bifurcation behavior. Results from fractional differential equations and bifurcation theory will be used to derive sufficient conditions for the occurrence of such dynamic transitions. A stable numerical scheme will be developed for numerical simulations. These will allow validating the obtained results and assessing the impact of the fractional-order parameter on the model’s quantitative dynamics.
Desired Skills: Basics of dynamical systems, Fractional calculus, MATLAB
Mentor: Prof. Hamadjam Abboubakar
Project 2
Title: Monetary Policy, Financial Development, and Renewable Energy Transition: A Panel Analysis
Summary: The aim of this project is to investigate the impact of monetary policy conditions on the development of renewable energy across countries using panel data. The study focuses on understanding how macroeconomic factors such as inflation, money supply, and domestic credit influence investments in renewable energy and the overall energy transition process. The research will examine the transmission mechanisms through which monetary policy affects renewable energy development, particularly via financial development and investment channels. It will analyze whether expansionary monetary conditions characterized by increased liquidity and credit availability facilitate the growth of renewable energy consumption, and whether macroeconomic instability acts as a constraint on long-term clean energy investments. Advanced panel econometric techniques will be employed, including fixed effects, random effects, and dynamic panel estimation methods such as Generalized
Method of Moments (GMM), to address issues of endogeneity and unobserved heterogeneity. The study will also incorporate interaction effects and nonlinear specifications to capture the conditional impact of financial development on the relationship between monetary policy and renewable energy adoption. The project aims to provide empirical evidence on the role of macroeconomic policy in supporting sustainable energy transitions and to derive policy-relevant insights for promoting renewable energy through stable, supportive financial environments.
Desired Skills: Basic econometrics, EViews, Stata
Mentor: Dr. Kolati Yeliyya
Project 3
Title: Mathematical Modeling of Fractional-Order Ecosystem Models
Summary: The aim of this project is to develop and analyze mathematical models of ecosystems using fractional-order calculus. The study will focus on understanding how key ecological parameters such as growth rates, carrying capacities, interaction coefficients, and environmental factors influence the dynamics of species populations. Special attention will be given to the role of memory effects and hereditary properties introduced by fractional differential equations, which provide a more realistic representation of ecological processes. The project will derive conditions for stability, equilibrium, and dynamic behaviors such as oscillations or complex population patterns. In addition, it aims to combine theoretical analysis with numerical simulations and computational implementation to illustrate how fractional-order ecosystem models can be applied to real-world environmental systems and resource management problems.
Desired Skills: Basics of differential equations, ecological modeling, MATLAB
Mentor: Prof. Vedat Suat Erturk
Project 4
Title: Bifurcation Analysis and Numerical Implementation of Fractional-Order Neural Networks
Summary: The aim of this project is to investigate the bifurcation behavior of fractional-order neural networks using modern tools from nonlinear dynamics and fractional calculus. The study will focus on identifying how changes in system parameters, delays, or connection strengths can lead to qualitative changes in system behavior such as oscillations, periodic solutions, or chaotic responses. Results from fractional differential equations and bifurcation theory will be used to derive sufficient conditions for the occurrence of such dynamic transitions. In addition, the project seeks to combine theoretical analysis, numerical simulations, and practical implementation to demonstrate the applicability of fractional-order neural network models in real-world intelligent systems and engineering applications.
Desired Skills: Basics of neural networks, MATLAB
Mentor: Prof. Pushpendra Kumar
Project 5
Title: Exploring Oscillatory Behavior in Dynamic Equations on Time Scales
Summary: This project aims to explore the oscillatory behavior of dynamic equations within the framework of time-scale calculus, which unifies continuous and discrete analysis. The study focuses on understanding how solutions of dynamic equations exhibit oscillatory behavior under different conditions and parameters.
Participants will learn to apply modern qualitative analysis techniques, such as Riccati transformations, comparison theorems, and inequality methods, to establish oscillation criteria. The project will also emphasize interpreting results through examples and developing analytical thinking.
This program integrates theoretical concepts with problem-solving approaches, enabling students to gain exposure to current research directions in dynamic equations and their applications in science and engineering.
Desired Skills: Basic knowledge of differential/difference equations
– Familiarity with MATLAB (preferred but not mandatory)
Mentor: Dr. Arundhathi Sivakumar
Project 6
Title: Fractional Stochastic Differential Equations: Theory, Stability, and Applications to Real-World Systems
Summary: This project focuses on recent theoretical and computational advances in fractional stochastic differential equations (FSDEs) and their applications to real-world complex systems. It investigates how fractional calculus and stochastic modeling can be combined to better represent systems with memory, hereditary behavior, and random uncertainty than classical models. The study emphasizes key mathematical aspects, including existence, uniqueness, stability analysis, and numerical solution techniques for FSDEs. Applications include epidemiology, finance, engineering, biological systems, and artificial intelligence, where uncertainty and long-term dependencies play crucial roles. The project aims to bridge modern mathematical theory with practical modeling challenges, providing innovative tools for analyzing dynamic systems under uncertainty.
Desired Skills: Basic knowledge of differential/difference equations, MATLAB
Mentor: Dr. P. Kalamani
Project 7
Title: Mathematical Modeling of Memory-Dependent Disease Dynamics Using Fractional Differential Equations
Summary: The aim of this project is to develop and analyze a mathematical model for infectious disease transmission using fractional-order calculus. Unlike classical integer-order models, fractional differential equations incorporate memory effects, allowing the system to account for past states of infection, recovery, and immunity.
The study will focus on understanding how epidemiological parameters such as transmission rate, recovery rate, incubation delay, and environmental influences affect the spread of disease over time. Special attention will be given to the role of memory in capturing realistic disease progression, especially when immunity wanes or delayed responses occur.
The project will derive conditions for equilibrium and stability of the disease-free and endemic states, and investigate dynamic behaviors such as persistence, oscillations, and threshold conditions. Numerical simulations will be carried out to illustrate how fractional-order models differ from classical models and provide better insights into real-world disease control strategies.
Desired Skills: Basics of differential equations, Mathematical modeling, MATLAB
Mentor: Dr. R. Sreedharan
What Participants Will Gain
- Exposure to Real Research Work
- Guidance from Experienced Mentors
- Problem Solving & Analytical Skills
- Technical Writing Experience
- Project Report / Presentation Experience
- Research Internship Completion Certificate
Certificate
Participants who successfully complete the internship requirements will receive an official:
ProfVista Summer Research Internship Completion Certificate
signed by:
- Head, ProfVista
- Project Mentor
Selection Process
Selection will be based on:
- Interest in the Project Topic
- Academic Motivation
- Basic Background Suitability
- Availability of Seats
Important Dates
Application Opens: 28th April, 2026
Last Date to Apply: 10th May, 2026
Result Announcement: 13th May, 2026
Internship Starts: 20th May, 2026
How to Apply
Interested candidates can apply through the official application form:
Apply Here:
Contact
For any queries:
ProfVista
Email: profvistateam@gmail.com
Website: https://profvista.com/
Note
This is an independent academic initiative by ProfVista, conducted online for educational and skill development purposes.