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An Exhaustive Treatment of Generalized Kolmogorov PDEs

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  • Sameerah Jamal

Abstract

A generalized partial differential equation (PDE) of Kolmogorov type featuring power law diffusion is examined. Our principal objective is to uncover transformations that simplify these equations. Moreover, we establish a supplementary condition that allows us to specify the underlying drift function. We also find exhaustive criteria for the power law parameter. The transformations are non trivial and involve special functions such as the hypergeometric, Bessel, modified Bessel, Whittaker, and hyperbolic tangent functions. As an immediate outcome, the method facilitates the construction of fundamental solutions for every equation of the class.PACS: 42.62.Be; 87.10.Ed; 04.20.ExMSC2020 Classification: 35K05, 35K15, 35Q92

Suggested Citation

  • Sameerah Jamal, 2026. "An Exhaustive Treatment of Generalized Kolmogorov PDEs," Abstract and Applied Analysis, Hindawi, vol. 2026, pages 1-8, August.
    • Handle: RePEc:hin:jnlaaa:4230441
    DOI: 10.1155/aaa/4230441
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