Numerical Investigation with Stability Assessment of Semi-Analytical Scheme for Time-Fractional Order Heat Type Emden-Fowler Equations

In the present paper, time-fractional order linear and nonlinear heat type Emden-Fowler equations are reformulated from existing classical equations by applying Caputo-Fabrizio time-fractional derivative. Then, a semi-analytical scheme, that is an amalgamation of Laplace transformation and Picard’s iterative technique, is exploited to simulate singular initial value problems for corresponding time-fractional order heat type Emden-Fowler equations. Further, the stability of developed scheme is also assessed by exploiting R-stable mapping and Banach contraction principle. Numerical results, error estimation, and comparison of obtained results with exact solutions are presented through graphs and tables to exhibit the efficiency of time-fractional order derivative and implemented semi-analytical scheme.