In this study, the so-called generalized differential transform method (GDTM) is developed to derive a semi- analytical solution for fractional partial differential equations which involves Riesz space fractional derivative. We focus primarily on implementing the novel algorithm to fractional telegraph equation with Riesz space-fractional derivative. Some theorems are presented to obtain new algorithm, as well as the error bound is found. This method is dealing with separating the main equation into sub-equations and applying transformation for sub-equations to attain compatible recurrence relations. This process will allow to obtain semi-analytical solution using inverse transformation. To illustrate the reliability and capability of the method, some examples are provided. The results reveal that the algorithm is very effective and uncomplicated.
Citation: S. Mohammadian, Y. Mahmoudi, F. D. Saei. Solution of fractional telegraph equation with Riesz space-fractional derivative[J]. AIMS Mathematics, 2019, 4(6): 1664-1683. doi: 10.3934/math.2019.6.1664
In this study, the so-called generalized differential transform method (GDTM) is developed to derive a semi- analytical solution for fractional partial differential equations which involves Riesz space fractional derivative. We focus primarily on implementing the novel algorithm to fractional telegraph equation with Riesz space-fractional derivative. Some theorems are presented to obtain new algorithm, as well as the error bound is found. This method is dealing with separating the main equation into sub-equations and applying transformation for sub-equations to attain compatible recurrence relations. This process will allow to obtain semi-analytical solution using inverse transformation. To illustrate the reliability and capability of the method, some examples are provided. The results reveal that the algorithm is very effective and uncomplicated.
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S. Mohammadian, Y. Mahmoudi, F. D. Saei. Solution of fractional telegraph equation with Riesz space-fractional derivative[J]. AIMS Mathematics, 2019, 4(6): 1664-1683. doi: 10.3934/math.2019.6.1664
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