On application of fractional calculus: Exact and approximate solutions for drying and wetting of rivers

Mathematical models for rivers differ according to the properties of the river. these models can be classified into drying–wetting,motion,masses,resources,and so on. this paper studies a system for practical water level prognostication and prediction during dry–wet seasons at the terengganu river. the mathematical model is a generalized master equation based on fractional calculus to obtain one-dimensional shallow water equations. we introduce two exact solutions for the proposed model. the first describes the drying condition of the river,and the second characterizes the wetting status. the actual data show the effectiveness of the new model. © 2015 pakistan journal of statistics.