Existence and uniqueness results for a smoking model with determination and education in the frame of non-singular derivatives

Abstract

These days, it is widely known that smoking causes numerous diseases, as well as resulting in many avoidable losses of life globally, and therefore encumbers the society with enormous unnecessary burdens. The aim of this study is to examine in-depth a smoking model that is mainly influenced by determination and educational actions via CF and AB derivatives. For both fractional order models, the fixed point method is used, which allows us to follow the proof of existence and the results of uniqueness. The effective properties of the above-mentioned fractional models are theoretically exhibited, their results are confirmed by numerical graphs by various fractional orders.

1. Introduction. Today, it is widely recognized that smoking does not bring about any benefits; on the contrary, each and every segment of the society is now aware of the numerous hazards that smoking engenders. For instance, your skin becomes deprived of moisture and elasticity, you become more likely to suffer from hypertension, your DNA becomes prone to detrimental effects, your immune system is rendered weaker, and you come face to face with worrisome issues involving economy, pregnancy, overall health, risk of untimely death, and so on. Moreover, many types of cancer, such as lung, mouth, and throat cancers take their source from the hazardous but often-unseen impact of smoking on our health according to researchers. In brief, the hazards originating from the smoking habit result in serious complications in both individual and social spheres. It has been formidably anticipated that no fewer than 7 million people lose their lives due to smoking-related problems every year worldwide. Taking all of these unfavorable facts into consideration, scientists from a multitude of fields seek to vanquish this dangerous habit so that they may expect to extend the health span of human beings. And many of those researchers concentrate on mathematical models to demonstrate the most.