Nonlinear Differential Equations in Physics

Santanu Saha Ray is Professor and Head of the Department of Mathematics, National Institute of Technology Rourkela, Odisha, India. An elected Fellow of the Institute of Mathematics and its Applications, UK, since 2018, Prof. Saha Ray is also a member of the Society for Industrial and Applied Mathematics (SIAM), American Mathematical Society (AMS) and the International Association of Engineers (IAENG). With over 18 years of experience in teaching undergraduate and graduate students and 17 years of research in mathematics, his focus areas are fractional calculus, differential equations, wavelet transforms, stochastic differential equations, integral equations, nuclear reactor kinetics with simulation, numerical analysis, operations research, mathematical modeling, mathematical physics, and computer applications.  The editor-in-chief of the International Journal of Applied and Computational Mathematics and associate editor of Mathematical Sciences (both published by Springer), Prof. Saha Ray has published research papers in various international journals of repute. In addition, he has authored six books: one with Springer and five with other publishers—Graph Theory with Algorithms and Its Applications: In Applied Science and Technology (Springer); Fractional Calculus with Applications for Nuclear Reactor Dynamics; Numerical Analysis with Algorithms and Programming; Wavelet Methods for Solving Partial Differential Equations and Fractional Differential Equations; Generalized Fractional Order Differential Equations Arising in Physical Models; and Novel Methods for Solving Linear and Nonlinear Integral Equations (with other publishers). He has served as principal investigator for various sponsored research projects funded by government agencies. He received an IOP Publishing Top Cited Author Award in 2018, which recognizes outstandingauthors using citations recorded in Web of Science.

1. Mathematical Preliminaries.- 2. New Approaches for Decomposition Method for the Solution of Differential Equations.- 3. Numerical Solution of Fractional Differential Equations by using New Wavelet Operational Matrix of General Order.- 4. Numerical Solutions of Riesz Fractional Partial Differential Equations.- 5. New Exact Solutions of Fractional Order Partial Differential Equations.- 6. An Investigation for New Double Periodic Solutions of Coupled Schrödinger-Boussinesq Equations.- 7. New Techniques for Fractional Reduced Differential Transform Method.- 7. A Novel Approach with Time-Splitting Fourier Spectral Method for Riesz Fractional Differential Equations.- 9. Numerical Simulation of Stochastic Point Kinetic Equation in the Dynamical System of Nuclear Reactor.