In this article, a new numerical scheme space Spectral time Fractional Adam Bashforth Moulton method for the solution of fractional partial differential equations is offered. The proposed method is obtained by modifying, in a suitable way; the spectral technique and the method of lines. The attention is focused on the stability properties and hence an elegant stability analysis for the current approach is also provided. Finally, two examples are presented to illustrate the effectiveness of the reported method. Obtained results confirm the convergence and spectral accuracy of the proposed method in both space and time. In addition, a comparison with the existing studies is also made as a limiting case of the considered problem at the end and found in good agreement.
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Sohail et al. (2017) studied this question.