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 beta and -beta are in strong agreement with the field images of selected outcrop sections. The memory effect is also shown with different values of alpha. The results revealed that the mathematical model better explains the geological processes. (C) 2020 The Author(s). Published by Elsevier B.V.