Effect of Fractional Order Time Derivative on the Out-Diffusion Profiles During Degassing a Thin Plate in Vacuum

Authors A. Souigat1 , Z. Korichi1 , M.E. Mezabia2, Y. Benkrima1 , M.T. Meftah3

1Ecole Normale Supérieure de Ouargla, 30000 Ouargla, Algeria

2Laboratoire de Mathématiques Appliquées, Kasdi Merbah University, 30000 Ouargla, Algeria

3Department of Physics, LRPPS Laboratory, Kasdi Merbah University, 30000 Ouargla, Algeria

Е-mail souigataek@gmail.com
Issue Volume 15, Year 2023, Number 2
Dates Received 25 January 2023; revised manuscript received 14 April 2023; published online 27 April 2023
Citation A. Souigat, Z. Korichi, et al., J. Nano- Electron. Phys. 15 No 2, 02011 (2023)
DOI https://doi.org/10.21272/jnep.15(2).02011
PACS Number(s) 42.90. + p, 45.10.Hj, 66.30. – h
Keywords Fractional derivative, Caputo-Fabrizio, Diffusion equation, Degassing a thin plate.

Fractional calculation methods and their applications in various scientific fields have aroused great interest in recent years. They have been used in the modeling of many physical problems, chemical processes and engineering. Recently, Caputo-Fabrizio proposed a new fractional order derivative without singular kernel, this new operator is suitable for the Laplace transformation and capable of describing physical behavior at different scales. In order to further investigate the possible application of this new operator, we used it to study the effect of fractional order time derivative on the out-diffusion profiles during degassing a thin plate in vacuum. In this work we modulate the impurity transport in the material during degassing by the time fractional diffusion equation, taking into account the Caputo-Fabrizio derivative, and we treated it by using the separation of variables method. An exact solution was obtained, depends on the time fractional-order derivative alpha. We observed that alpha plays an important role in the numerical simulations and it has an effect on the out-diffusion profiles, where the degassing is faster as alpha approaches 1, and the degassing is slow as alpha approaches zero.

List of References