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.

中文翻译：

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非奇异导数框架下具有确定性和教育性的吸烟模型的存在性和唯一性结果

如今，众所周知，吸烟会导致多种疾病，并在全球范围内造成许多本可以避免的生命损失，因此给社会带来了巨大的不必要负担。本研究的目的是深入研究一个吸烟模型，该模型主要受通过 CF 和 AB 衍生物的决心和教育行动的影响。对于这两种分数阶模型，都使用了不动点方法，这使我们能够遵循存在性证明和唯一性结果。上述分数模型的有效性质在理论上得到了展示，它们的结果由各种分数阶的数值图证实。