I am currently working as a Senior Research Fellow in Applied Mathematics at the University of Hyderabad under the supervision of Prof. Saroj Panigrahi. My research primarily revolves around nonlinear fractional boundary value problems, which are mathematical models involving fractional-order differential equations subject to boundary conditions. These problems have gained significant attention in recent years due to their ability to describe complex physical, biological, and engineering processes more accurately than classical integer-order models.

Within this broad area, my specific focus is on the theoretical aspects concerning the existence and multiplicity of positive solutions. In other words, I investigate whether such problems admit one or more meaningful solutions, particularly solutions that are positive and thus physically relevant in many applications (for instance, population dynamics, heat transfer, viscoelasticity, and fluid flow).

To achieve this, I make use of the Hammerstein integral operator framework, which allows the reformulation of fractional boundary value problems into equivalent integral equations involving Green’s functions. This approach provides a powerful tool for studying the qualitative properties of solutions.

The mathematical techniques I employ are rooted in fixed point theories, which form the foundation for proving existence and multiplicity results. Specifically, I work with methods such as the Fixed Point Index Theory, the Leggett–Williams Fixed Point Theorem, and related fixed point principles. These theories not only establish the existence of solutions but also help in characterizing their number and nature under suitable conditions.

Overall, my research lies at the intersection of fractional calculus, functional analysis, and nonlinear analysis, with the aim of developing rigorous mathematical results that can also serve as a foundation for applications in real-world models.

Education

• Ph.D. in Applied Mathematics (2020 – Present)
  School of Mathematics and Statistics, University of Hyderabad, Hyderabad, Telangana

• M.Sc. in Mathematics and Computing  (2017 – 2019)                                                                                                                                                                                                        IIT Guwahati, Assam 

• B.Sc. in Mathematics (2014 – 2017)
  D.A.V. College, Kanpur Nagar, Uttar Pradesh 

• Intermediate (Class XII)
  Oxford Model Inter College, Kanpur Nagar, Uttar Pradesh
  
  

Research Interest

1. Nonlinear Analysis, Fixed Point Theory, Fractional Boundary Value Problems, and Delay Differential Equations.

Related to research

• Google Scholar 

• Orchid Id: 0009-0001-1721-4270