Solving for the random component time-fractional partial differential equations with the new Sumudu transform iterative method

The new Sumudu transform iterative method is implemented to get the approximate solutions of random component time-fractional partial differential equations with Caputo derivative. The parameters and the initial conditions of the random component time-fractional partial differential equations are analyzed with Gamma distribution. The expected values and variances of these solutions are calculated, and the graphs of the expected values and variances are plotted in Maple software. The results for the random component time-fractional partial differential equations with Gamma distribution are examined to investigate effects of this distribution on results. The numerical experiments indicate that this method is very effective.