Essential Criteria for Existence of Solution of a Modified-Abc Fractional Order Smoking Model
Ain Shams Engineering Journal/Ain Shams Engineering Journal(2024)
Abstract
Drug usage has always been a top concern for parents and government officials, harming younger people's lives in circumstances that cannot be undone. This paper considers a modified ABC-fractional-order Ice-smoking dynamical system for the theoretical and numerical results. In the theoretical aspect, we study the solution existence, uniqueness work, and Hyers-Ulam (HU) stability of the presumed extended fractional order dynamical system of Ice smoking. Recursive sequences that follow one another are designed to verify the existence of a solution to the provided Ice-smoking model. Functional analysis principles and findings are applied to showcase the uniqueness of the solution and the stability under the Hyers-Ulam (HU) framework. We offer simulations and a comparison by graphs by using Lagrange polynomials. The simulations demonstrate the scheme's applicability, future forecasting, and validations of the results of modified ABC-fractional orders.
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Key words
Modified ABC modeling,Existence of solutions,Stability results,Lagrange polynomials,Graphical representation
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