A Novel Mathematical Investigation of Synthetic Precipitation Employing Diverse Variable -Order Non-linear Fractional Derivatives

Abstract

An inadequate rainfall pattern results in water scarcity, groundwater depletion, pollution escalation, and ecological disruption. Addressing these challenges, comprehensive water management strategies will be necessary to ensure sustainability. This paper proposes a nonlinear fractional variable-order model of artificial rain making in the sense of Liouville-Caputo, Caputo-Fabrizio and Atangana –Baleanu fractional derivatives .The existence and uniqueness of fractional solutions has been established and numerical simulations have been carried out to study the influence of different parameters on the process of artificial rainmaking leading to rainfall.