Abstract : Because of its computing efficiency, precision, and relative simplicity, the Reduced Differential Transform Method (RDTM) has become a powerful analytical tool for solving many types of partial differential equations (PDEs). Our focus here is on time fractional nonlinear PDEs, a large and important class of mathematical models, and how RDTM may be applied to solve them. Traditional solution methods are challenged by the complicated behaviour of these equations, which emerge in different scientific areas including physics, engineering, and biology. This study lays out a full mathematical scheme for solving time fractional nonlinear PDEs using RDTM. First, we provide an overview of RDTM and how it has been modified to deal with fractional derivatives. Afterwards, we describe in detail the process for applying RDTM to nonlinear PDEs with fractional temporal derivatives, elaborating on important computational details and algorithmic stages. We show numerical examples of the methodology in action, showing that it efficiently and accurately solves various time fractional nonlinear PDE types. In addition, we go over the computational details of using RDTM to solve time fractional nonlinear PDEs. In sum, the paper meticulously lays out the theoretical groundwork and computational details of using RDTM to solve time fractional nonlinear PDEs. The offered methodology provides a useful resource for academics and professionals in quest of effective answers to complicated mathematical models found in many scientific and engineering domains. Keywords: Mathematical Framework, Fractional Derivatives, Analytical Solution, Efficiency
Cite : Singh, P. P., Singh, O., & Raghav, S. (2024). Reduced Differential Transform Method For Time Fractional Nonlinear Pdes: Mathematical Framework And Computational Aspects (1st ed., pp. 155-163). Noble Science Press. https://doi.org/10.52458/9788197112492.nsp.2024.eb.ch-16
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