An Adaptive Hybrid Differential Transform Method for Variable-Order Fractional Reaction-Diffusion Models with Applications to Tumour Growth and Heat Transfer

Pradnya S. Aher, Ashok P. Bhadane, Avinash V. Khambayat

Abstract: In this paper, we propose an Adaptive Hybrid Fractional Differential Transform Method (AHFDTM) for solving nonlinear variable-order fractional reaction-diffusion equations arising in tumour growth and heat transfer phenomena. The proposed method combines the Differential Transform Method (DTM) with an adaptive weighting strategy that automatically adjusts the transform coefficients according to the local fractional order. Existence, uniqueness, convergence, and stability are proved. The numerical experiments demonstrate that AHFDTM has less error and converges more quickly than FRDTM, ADM, HPM, and VIM. The applications to a fractional tumour growth model and a fractional bioheat transfer equation confirm the effectiveness of the proposed scheme.

Keywords: Fractional differential equations, Differential Transform Method, Variable-order derivatives, Reaction?diffusion equations, Tumour growth, Heat transfer

How to Cite?: Pradnya S. Aher, Ashok P. Bhadane, Avinash V. Khambayat, "An Adaptive Hybrid Differential Transform Method for Variable-Order Fractional Reaction-Diffusion Models with Applications to Tumour Growth and Heat Transfer", Volume 15 Issue 7, July 2026, International Journal of Science and Research (IJSR), Pages: 861-868, https://www.ijsr.net/getabstract.php?paperid=SR26708113231, DOI: https://dx.doi.org/10.21275/SR26708113231

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