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Fractional Adomian J-Transform Method for Time-Fractional Diffusion-Wave Equations: Theory and Applications

Author

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  • Nazek A. Obeidat
  • Mahmoud S. Rawashdeh
  • Ali M. Baniatta

Abstract

In this research, we introduce the fractional Adomian J-transform method FAJM, which functions as a robust hybrid analytical-numerical framework. Diverging from traditional transform techniques, the FAJM leverages the specific scaling attributes of the J-transform to streamline the inversion of nonlocal fractional operators. We establish a comprehensive mathematical structure by deriving original transform identities in Theorems and defining rigorous convergence criteria and error constraints in Theorems. Our comparative assessment indicates that the FAJM provides superior computational efficiency when managing power-law kernels and enhances symbolic processing. The efficacy of this approach is confirmed through various fractional diffusion scenarios, showing enhanced convergence speed compared to standard LADM and SADM models.

Suggested Citation

  • Nazek A. Obeidat & Mahmoud S. Rawashdeh & Ali M. Baniatta, 2026. "Fractional Adomian J-Transform Method for Time-Fractional Diffusion-Wave Equations: Theory and Applications," Journal of Mathematics, Hindawi, vol. 2026, pages 1-18, May.
    • Handle: RePEc:hin:jjmath:9121715
    DOI: 10.1155/jom/9121715
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