Pathway to Fractional Integrals, Fractional Differential Equations and the Role of H-function

Arak M. Mathai; Hans J. Haubold

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arXiv · 2405.11050

Pathway to Fractional Integrals, Fractional Differential Equations and the Role of H-function

Arak M. Mathai·Hans J. Haubold

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Abstract

The pathway model for the real scalar variable case is re-explored and its connections to fractional integrals, solutions of fractional differential equations, Tsallis statistics and superstatistics in statistical mechanics, reaction-rate probability integral, Kraetzel transform, and pathway transform are explored. It is shown that the common thread in these connections is the H-function representations. The pathway parameter is shown to be connected to the fractional order in fractional integrals and fractional differential equations.

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Arak M. Mathai, Hans J. Haubold. 2024-05-17. Pathway to Fractional Integrals, Fractional Differential Equations and the Role of H-function. https://arxiv.org/abs/2405.11050

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