A Fractional Model for Diffusion Equation Using Generalized Fick??s Law: Exact Solution with Laplace Transform

Nadeem Ahmad Sheikh, Dennis Ling Chuan Ching, Ilyas Khan, Afnan Ahmad, Syed Ammad

Abstract


Fractional calculus is the generalization of classical calculus. Many researchers have used different definitions in their studies. The most common definition is Caputo fractional derivatives operator. In this article the concentration equation is converted to fractional form using the generalized Fick??s law. The fractional partial differential is then transformed with an appropriate transformation. The Laplace and Fourier sine transformations are jointly used to solve the equation. The impact of fractional parameter and Schmidt number is checked on the concentration profile and presented in graphs and tabular form. The results show that diffusion is decreasing with increasing values of Schmidt number.


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DOI: https://doi.org/10.33959/cuijca.v3i2.28

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