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.
In this paper, the nonlinear system of local fractional partial differential equations is solved via local fractional Elzaki transform decomposition method. The local fractional Elzaki decomposition transform method combines a local fractional Elzaki transform and the Adomian decomposition method. Applications related to the nonlinear system of local fractional partial differential equations are presented.
In this study, the solutions of random partial differential equations are examined. The parameters and the initial conditions of the random component partial differential equations are investigated with Beta distribution. A few examples are given to illustrate the efficiency of the solutions obtained with the random Differential Transformation Method (rDTM). Functions for the expected values and the variances of the approximate analytical solutions of the random equations are obtained. Random Differential Transformation Method is applied to examine the solutions of these partial differential equations and MAPLE software is used for the finding the solutions and drawing the figures. Also the Laplace-Padé Method is used to improve the convergence of the solutions. The results for the random component partial differential equations with Beta distribution are analysed to investigate effects of this distribution on the results. Random characteristics of the equations are compared with the results of the deterministic partial differential equations. The efficiency of the method for the random component partial differential equations is investigated by comparing the formulas for the expected values and variances with results from the simulations of the random equations.
Some nonlinear time-fractional partial differential equations are solved by homotopy perturbation Elzaki transform method. The fractional derivatives are defined in the Caputo sense. The applications are examined by homotopy perturbation Elzaki transform method. Besides, the graphs of the solutions are plotted in the MAPLE software. Also, absolute error comparison of homotopy perturbation Elzaki transform method and homotopy perturbation Sumudu transform method solutions with the exact solution of nonlinear time-fractional partial differential equations is presented. In addition, this absolute error comparison is indicated in the tables. The novelty of this article is the first analysis of both the gas dynamics equation of Caputo fractional order and the Klein-Gordon equation of Caputo fractional order via this method. Thus, homotopy perturbation Elzaki transform method is quick and effective in obtaining the analytical solutions of time-fractional partial differential equations.
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