Investigating Solutions of the Noyes-Whitney Dynamic Equation via Proportional Fractional Derivative

Authors : Tuba Gülşen, Melek Dönmez

Pages : 35-41

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Publication Date : 2024-03-28

Article Type : Research Paper

Abstract :The dynamics of solid material dissolving in a solvent are fundamentally described by the Noyes-Whitney equation. For the purpose of simulating intricate processes with memory effects and non-local behaviors, fractional calculus offers a strong foundation. We explore the effects of memory and non-locality on dissolution kinetics by solving the Noyes-Whitney equation using fractional derivatives. By means of mathematical analysis, we provide insights into the dissolving processes in chemical engineering and pharmaceutical applications by clarifying the behavior of the Noyes-Whitney equation with proportional fractional derivative. In this study, after discussing the characteristics and theories of the proportional fractional derivative on a time scale, we solve the proportional fractional Noyes-Whitney dynamic equation in the presence of the initial condition and give several examples on various time scales via the proportional fractional derivative.
Keywords : Noyes Whitney dinamik denklemi, kesirli hesap, oransal kesirli türev