• P-ISSN 0974-6846 E-ISSN 0974-5645

# Indian Journal of Science and Technology

## Article

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Indian Journal of Science and Technology

Year: 2021, Volume: 14, Issue: 48, Pages: 3509-3524

Original Article

## Mathematical Analysis of Pluviculture in the Frame of Caputo Fractional Derivative

Received Date:20 October 2021, Accepted Date:27 November 2021, Published Date:28 December 2021

## 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

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