A generalized model for quantitative analysis of sediments loss: A Caputo time fractional model

Abstract

Sediment loss is an indispensable geological phenomenon that determines the reduction of mass in time interval with the differential influence of controlling factors. In this study, the competence of rocks is considered as a controlling factor while weathering and erosion are termed as the decaying parameter. Attributed to the reduction of the total mass in unit time. A mathematical model is [proposed for the above-mentioned phenomenon and generalized using the Caputo fractional derivatives approach to better understand and predict the sediment loss. The model is solved for exact solutions using the Laplace transform technique. The results obtained for β and -β are in strong agreement with the field images of selected outcrop sections. The memory effect is also shown with different values of αThe results revealed that the mathematical model better explains the geological processes.

Keywords

• Sediment loss
• Decaying parameter
• Controlling factor
• Fractional derivatives
• Exact solutions