Symmetry analysis, exact solutions and numerical approximations for the space-time Carleman equation in nonlinear dynamical systems

Abstract

This work presents an investigation and analysis for the space-time Carleman equation (STCE) in nonlinear dynamical systems. We compute the point symmetries, similarity variable, similarity transformation for STCE with Riemann-Liouville (RL) derivative and reduce STCE to ordinary differential equation (ODE) of fractional order. The exact solutions with conformable derivative are obtained via the generalized Bernoulli (GB) sub-ODE method. The well known residual power series technique (RPST) is used to compute the corresponding approximate solutions for the obtained exact solution. We then verify the convergence analysis and error estimate of RPST. Numerical simulations of the results are shown with the aid of graphical illustrations and tables. We prove that the RPST is very efficient for investigating the numerical approximations for a system of fractional differential equations.