Uttam Ghosh

Bio: Uttam Ghosh is an academic researcher from University of Calcutta. The author has contributed to research in topics: Fractional calculus & Differential equation. The author has an hindex of 12, co-authored 77 publications receiving 370 citations.

Analytical solution with tanh-method and fractional sub-equation method for non-linear partial differential equations and corresponding fractional differential equation composed with Jumarie fractional derivative

Abstract: The solution of non-linear differential equation, non-linear partial differential equation and non-linear fractional differential equation is current research in Applied Science. Here tanh-method and Fractional Sub-Equation methods are used to solve three non-linear differential equations and the corresponding fractional differential equation. The fractional differential equations here are composed with Jumarie fractional derivative. Both the solution is obtained in analytical traveling wave solution form. We have not come across solutions of these equations reported anywhere earlier.

Stability and Bifurcation Analysis of Logistically Grown SIR Model with External Infection Effect of the Susceptible Class and Effect of Loss of Immunity of the Recovered Class

Abstract: In this paper we consider an SIR model with logistic growth rate of susceptible where rate of incidence is directly affected by inhibitory factors or social or psychological factors and infection through interaction and external source also taken into consideration. In our model three equilibrium points are obtained under different conditions. One of them is trivial equilibrium point which always exists and unstable in nature in all circumstance. The other two are endemic equilibrium points exist under certain conditions and one of them becomes non-feasible under another condition. Here we examine the hopf-bifurcation depending on carrying capacity. Finally numerical simulations are done.

Analytical Solutions of Classical and Fractional KP-Burger Equation and Coupled KdV Equation

Abstract: Evaluation of analytical solutions of non-linear partial differential equations (both classical and fractional) is a rising subject in Applied Mathematics because its applications in Physical biological and social sciences. In this paper we have used generalized Tanh method to find the exact solution of KP-Burger equation and coupled KdV equation. The fractional Sub-equation method has been used to find the solution of fractional KP-Burger equation and fractional coupled KdV equations. The exact solution obtained by fractional sub-equation method reduces to classical solution when order of fractional derivative tends to one. Finally numerical simulation has done. The numerical simulation justifies that the solutions of two fractional differential equations reduces to shock solution for KP-Burger equation and soliton solution for coupled KdV equations when order of derivative tends to one.

Differential Equations and Dynamical Systems

Abstract: Series Preface * Preface to the Third Edition * 1 Linear Systems * 2 Nonlinear Systems: Local Theory * 3 Nonlinear Systems: Global Theory * 4 Nonlinear Systems: Bifurcation Theory * References * Index

Encyclopedia of Quality of Life and Well-Being Research

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