Effect of fractional temporal variation on the vibration of waves on elastic substrates with spatial non-homogeneity

AIMS Mathematics

article

Ahmed SM Alzaidi¹  Ali M Mubaraki¹  Rahmatullah Ibrahim Nuruddeen² 

[1] Department of Mathematics and Statistics, Collage of Science, Taif University;Department of Mathematics, Faculty of Science, Federal University Dutse

关键词: Laplace transform;    non-homogeneous substrates;    elastic waves;    fractional order;   

DOI  :  10.3934/math.2022757

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

The current manuscript examines the effect of the fractional temporal variation on the vibration of waves on non-homogeneous elastic substrates by applying the Laplace integral transform and the asymptotic approach. Four different non-homogeneities, including linear and exponential forms, are considered and scrutinized. In the end, it is reported that the fractional temporal variation significantly affects the respective vibrational fields greatly as the vibrations increase with a decrease in the fractional-order $\mu$. Besides, the two approaches employed for the cylindrical substrates are also shown to be in good agreement for very small non-homogeneity parameter $\alpha$. More so, the present study is set to play a vital role in the fields of material science, and non-homogenization processes to state a few.

【 授权许可】

CC BY