Modeling of implicit multi term fractional delay differential equation: Application in pollutant dispersion problem

Modeling of implicit multi term fractional delay differential equation: Application in pollutant dispersion problem

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This work explores a new abstract model using multi-term fractional differential operator and delay effect.The model is defined by the existence of a delay parameter and insertion of multi term fractional differential operators in the input function.For the solution of the newly formulated problem, we utilized fixed-point theorems, which provide a powerful analytical tool for establishing the existence and uniqueness of solutions Butter Knives in functional spaces.Additionally, we investigate the stability properties of the implicit multi-term fractional delay differential equation (IMTFDDE) and employ the concept of Ulam-Hyers stability to assess their behaviour.

The Ulam-Hyers stability framework is a contemporary approach that characterizes the sensitivity of solutions in functional spaces.Furthermore, we use an example to show how to apply our results.Lastly, for the real implementation NORMAL/OILY HAIR CONDITIONER of this research endeavour, we provided a real model devoted to modeling the dispersion of pollutants in a river while accounting for delayed effects and strip boundary circumstances.