A General Conformable Diffusion Equation

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DOI: https://doi.org/10.28924/2291-8639-24-2026-240
Published: Aug 3, 2026
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Bambang Hendriya Guswanto, Yuliyanti Dewi Lestari, Vera Nur Fadiya, Idha Sihwaningrum, Suroto Suroto, Ari Wardayani, Siti Rahmah Nurshiami, Najmah Istikaanah, Indra Herdiana, A General Conformable Diffusion Equation, Int. J. Anal. Appl., 24 (2026), 240.

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Bambang Hendriya Guswanto, Yuliyanti Dewi Lestari, Vera Nur Fadiya, Idha Sihwaningrum, Suroto Suroto, Ari Wardayani, Siti Rahmah Nurshiami, Najmah Istikaanah, Indra Herdiana

Abstract

We here derive a new mathematical model for a transport system in a diffusion process with involving general conformable fractional derivative. The model is called general conformable diffusion equation derived from continuous time random walk process considering stochastic aspects. The model is characterized by a function called fractional conformable function which has an intimate relationship with the waiting time of a cell to move in the diffusion process. Solutions to the general conformable diffusion equation are also studied. The application in modeling the transport system of chloride ions diffusing in non-saturated concretes is given to show that the general conformable diffusion equation can be used to model the diffusion process better by choosing a suitable fractional conformable function.

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