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 focuses on nonlinear fractional boundary value problems, which arise in modeling complex physical, biological, and engineering phenomena. In particular, I study the existence and multiplicity of positive solutions that are mathematically and physically meaningful. My work employs the Hammerstein integral operator framework to reformulate fractional problems into equivalent integral equations via Green’s functions. To establish rigorous results, I use tools from fixed point theory, including Fixed Point Index Theory and the Leggett–Williams Fixed Point Theorem. Overall, my research integrates fractional calculus, functional analysis, and nonlinear analysis to provide strong theoretical foundations for applied 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

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

Related to research

• Google Scholar 

• Orchid Id: 0009-0001-1721-4270