Fractional model of smoking with relapse and harmonic mean type incidence rate under Caputo operator

• Published in: Journal of applied mathematics & computing Vol. 69; no. 1; pp. 403 - 420
• Main Authors: Haidong, Qu, Rahman, Mati ur, Arfan, Muhammad
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2023; Springer Nature B.V
• Subjects: Applied mathematics; Computational Mathematics and Numerical Analysis; Exact solutions; Fixed points (mathematics); Integers; Mathematical and Computational Engineering; Mathematical models; Mathematics; Mathematics and Statistics; Mathematics of Computing; Original Research; Smoking; Theory of Computation; GABMM iterative technique; Smoking problem; Approximate solution; Existence of solution; 37N25; 37N30
• ISSN: 1598-5865; 1865-2085
• DOI: 10.1007/s12190-022-01747-6

In this manuscript, we have analyzed a new time non-integer order smoking model endowed with Caputo fractional type derivative operator. The model is composed of four compartmental agents of various smokers named as a potential smoker, Light smoker, Smoker and Quit smoker. The first attempt is about the qualitative study of the considered problem along with the existing result and the derivation of the unique solution by the application of the fixed point theory. Secondly, for the semi-analytical solution of the smoking model, a very famous technique of the Generalized Adams–Bashforth Moulton method is used. Numerical simulation for different integer and non-integer order laying between (0, 1) has been drawn using Matlab. For different initial data, the result of simulation depicts the solution of the considered model is stable and shows the convergence of a single point. Smaller fractional orders show good results in the framework of stability.