INDIAN JOURNAL OF SCIENCE AND TECHNOLOGY RESEARCH ARTICLE OPEN ACCESS Received: 20.10.2021 Accepted: 27.11.2021 Published: 28.12.2021 Citation: Achar SJ, Baishya C (2021) Mathematical Analysis of Pluviculture in the Frame of Caputo Fractional Derivative. Indian Journal of Science and Technology 14(48): 3509-3524. https://doi.org/ 10.17485/IJST/v14i48.1965 ∗ Corresponding author. sindhuachar6@gmail.com Funding: None Competing Interests: None Copyright: © 2021 Achar & Baishya. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee) ISSN Print: 0974-6846 Electronic: 0974-5645 Mathematical Analysis of Pluviculture in the Frame of Caputo Fractional Derivative Sindhu J Achar 1∗ , Chandrali Baishya 1 1 Department of Studies and Research in Mathematics, Tumkur University, Tumkur-572103, Karnataka, India 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 1 Introduction Rainmaking, also known as pluviculture, is the method of inducing precipitation artifcially. Tis is done to stave of drought and to save Earth from wider global warming. Tis 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. Te concept of ”pluviculture,” or the artifcial rain creations, has long history, both ancient and modern. Especially during the 19th and 20th centuries, it has excited the mind’s eye and brought forth enormous rainmaking techniques. 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. (2,3) Firstly, water vapors are converted to cloud https://www.indjst.org/ 3509