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In this study, we examine and using Laplace Transform as a way to find approximate solutions to multi-dimensional space and time fractional order problems and propose numerical algorithm for solving ([Formula: see text])-dimensional time and space fractional order heat like and time and space fractional wave-like equations. This method is a combination of Laplace Transform and iterative method. The fractional derivative is described in the Caputo sense. The results obtained by proposed scheme are compared with different other schemes. This scheme is found to be very efficient and effective for linear and nonlinear time and space fractional order problems.

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The new iterative method has been used to obtain the approximate solutions of time fractional damped Burger and time fractional Sharma-Tasso-Olver equations. Results obtained by the proposed method for different fractional-order derivatives are compared with those obtained by the fractional reduced differential transform method (FRDTM). The 2nd-order approximate solutions by the new iterative method are in good agreement with the exact solution as compared to the 5th-order solution by the FRDTM.

In the present article, the fractional order differential difference equation is solved by using the residual power series method. Residual power series method solutions for classical and fractional order are obtained in a series form showing good accuracy of the method. Illustrative models are considered to affirm the legitimacy of the technique. The accuracy of the chosen problems is represented by tables and plots which show good accuracy between the exact and assimilated solutions of the models.