Authors : Abdul Rahman Moutmaen; Hayatullah saeed; Shuja Kaheshzad

Volume/Issue : Volume 11 - 2026, Issue 4 - April

Google Scholar : https://tinyurl.com/4v7j7nx2

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DOI : https://doi.org/10.38124/ijisrt/26apr2253

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Abstract : Due to the intricacy of fractional derivatives and boundary conditions, finding trustworthy solutions for fractional partial differential equations (FPDEs) continues to be a significant challenge. In this research, a framework for effectively solving FPDEs using the Reduced Differential Transform Method (RDTM) is presented. Based on a straightforward recursive formulation, the proposed RDTM offers rapidly convergent analytical–approximate solutions without the need for discretization, linearization, or intricate integral computations. The accuracy and convergence of RDTM are methodically compared with those of ADM, HPM, RPS, and L-RPS. According to numerical studies, RDTM maintains computational simplicity while achieving greater numerical stability, faster convergence, and higher accuracy. The durability and efficacy of the proposed framework are confirmed by applications to fractional wave, telegraph, and Poisson equations, indicating its potential as a dependable tool for intricate fractional models in mathematical physics and engineering.

Keywords : Fractional PDEs; Reduced Differential Transform; Accuracy; Convergence.

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