FORECASTING THE BEHAVIOR OF FRACTIONAL MODEL OF EMDEN–FOWLER EQUATION WITH CAPUTO–KATUGAMPOLA MEMORY

Abstract

The main aim of this paper is to analyze the behavior of time-fractional Emden–Fowler (EF) equation associated with Caputo–Katugampola fractional derivative occurring in mathematical physics and astrophysics. A powerful analytical approach, which is an amalgamation of q-homotopy analysis approach and generalized Laplace transform with homotopy polynomials, is implemented to obtain approximate analytical solution of the time-fractional EF equation. Main advantage of this research work is that the implemented technique contains an auxiliary parameter to control the convergence region of obtained series solution. Some examples are considered to illustrate the accuracy and efficiency of the applied technique. Numerical results are demonstrated in the form of tabular and graphical representations.