Abstract
Objectives: Climate change is a major issue the mankind is facing in the present scenario. This is a consequence of global warming that result in the change in temperature and rainfall over a long period of time. In this work, we analyze the fractional mathematical model projecting pluviculture. The Caputo fractional derivative is incorporated for better analysis of this event. Also, we discuss the boundedness, existence and uniqueness of the solutions of the proposed system. Sufficient conditions required for existence of asymptotic stability are discussed. Method: We have used the generalized Adams- Bashforth-Moulton predictor-corrector technique to solve the pluviculture model. It is the linear multistep implicit method used to solve the system of equations. Findings: It is established that, the intensity of precipitation is enhanced by introducing the aerosols to the water vapor. The incorporation of the fractional derivatives strengthens the model in a more realistic way. The influence of some parameters and fractional derivative on the rain making process are numerically analyzed. Novelty: The incorporation of Caputo fractional derivative to the pluviculture model along with the two kinds of aerosols is the novel in the model. Keywords: Pluviculture; Aerosol; Caputo fractional derivative; AdamsBashforthMoulton technique Mathematics Subject Classification: 26A33; 92D30
Highlights
Rainmaking, known as pluviculture, is the method of inducing precipitation artificially
The pluviculture model with the fractional order is nowhere discussed. Keeping all these in view, in the present work, we have proposed a mathematical model including the two kinds of aerosols in the atmosphere leading to the precipitation incorporating the Caputo fractional derivative which is the novel in the model
By considering the previous results and values as that of in [15] along with other predicted values for the new parameters used in our present model, the dynamics of the model is studied by using generalized Adams-Bashforth-Moulton technique
Summary
Rainmaking, known as pluviculture, is the method of inducing precipitation artificially. This is done to stave off drought and to save Earth from wider global warming. This can be achieved using rockets or airplanes to sow to the clouds along with the catalysts like silver iodide, [1] dry ice and salt powder, to increase precipitation and mitigate farmland drought. Rain making is a prime and complex phenomenon in the environment. Several physicochemical processes such as agglomeration, nucleation, condensation and so on are involved in this process. Several physicochemical processes such as agglomeration, nucleation, condensation and so on are involved in this process. [2,3] Firstly, water vapors are converted to cloud
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