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About the Project

The main aim of this project work is to develop the invariant subspace and Lie group analysis method to solve the scalar and coupled system of nonlinear fractional ODEs and PDEs. So, this development will be helpful in systematically studying analytical solutions for scalar and coupled system of fractional-order ODEs and PDEs along with appropriate initial and boundary conditions in science and engineering. Therefore, I believe that the outcome of this research greatly benefits the scientific and engineering community, which would like to study or understand the dynamic behaviours of complex systems and materials in science and engineering that can model using either scalar or system of fractional PDEs. So, these investigations show that the Lie group analysis and invariant subspace methods are essential and effective powerful analytical tools for finding exact solutions of various scalar and coupled system of fractional nonlinear PDEs in science and engineering. Also, we can construct conservation laws using the obtained Lie point symmetries.

Department and Campus

Department of Mathematics, School of Physical Sciences, Coimbatore

Skillsets Preferred from Applicants

Good Percentage in B.Sc., and M.Sc.(Mathematics/Applied Mathematics) or CSIR-UGC- NET or GATE or SET.


Methods and Application of Nonlinear Differential Equations, Fractional Calculus and their Applications to Real World Problems, Application of Ordinary, Partial and Fractional Differential Equation to Diffusion Problems, Lie Group Analysis and Invariant Subspace Methods, Analytical Methods for Partial Differential Equations, Analytical Methods for Ordinary Differential Equations, Integral Transformation Methods, Conservation Laws, Lie Algebra
Dr. Prakash P

Assistant Professor
Department of Mathematics
School of Engineering, Coimbatore

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