Ecological balance model of effective utilization of agricultural water resources based on fractional differential equations

Abstract

Water is a key factor that controls the evolution of the ecosystem and restricts social and economic development. The rational allocation of water resources is the basis for the basin's sustainable use of water resources. The article uses fractional differential equations to discuss the increasingly prominent contradictions between supply and demand of agricultural water resources, serious pollution and overexploitation, the decline in groundwater level and water quality, low agricultural water efficiency, and serious waste from the perspective of sustainable development. Second, the article classifies the index system of the water resources carrying capacity evaluation model. Finally, model the resource balance of water supply and water demand in the irrigation area. The study found that the water quantity analysis and determination of the irrigation area will have important guiding significance for implementing the irrigation area's continued construction and water-saving transformation. The allocation and utilization of water resources in farmland irrigation areas will tend to be rationalized. This will greatly improve the water-saving efficiency of irrigation districts.

A Mini-Review on Recent Fractional Models for Agri-Food Problems

“…A hybrid scheme based on genetic algorithms and a simplex-based algorithm was adopted for parameter estimation. Evapotranspiration and the effective utilization of agricultural water resources were investigated in [40]. Here, the authors converted a model previously proposed in [43] into a time-fractional model.…”

An optimization method for studying fractional-order tuberculosis disease model via generalized Laguerre polynomials

“…Recently, various fields of science, engineering, and biochemistry have a growing interest in the fractional calculus field and its application (Hilfer 2000 ; Li 2022 ; Oldham 2010 ; Magin 2010 ; Ortigueira 2011 ). Gao1 et al.…”

Maximum Principle for Nonlinear Fractional Differential Equations with the Hilfer Derivative

“…Recently, the subject of fractional calculus has been extensively developed and studied by many academics due to its applications in numerous branches of applied sciences, technology, and engineering. Examples include engineering [1], ecology [2], biology [3], medicine [4], chemistry [5], animal science [6], finance [7], control theory [8], and other branches. In recent decades, Hilfer defined a generalized fractional derivative of Riemann-Liouville (R-L), which includes fractional derivatives of Caputo and R-L [9].…”