An approach for approximate solution of fractional-order smoking model with relapse class

作     者：Anwar Zeb Vedat Suat Erturk Umar Khan Gul Zaman Shaher Momani 

作者机构：Department of Mathematics COMSATS University Islamabad Abbottabad Campus Pakistan Department of Mathematics Faculty of Arts and Sciences Ondokuz Mayis University 55139 Samsun Turkey Department of Mathematics University of Malakand Chakdara Dir (Lower) KPK PakistantDepartment of Mathematics Faculty of Arts and Sciences Ondokuz Mayis University 55139 Samsun Turkey Department of Mathematics Faculty of Science The University of Jordan Amman 1195 Jordan Nonlinear Analysis and Applied Mathematics (NAAM)Research Group Department of Mathematics Faculty of Science King Abdulaziz University Jeddah 21589 Saudi Arabia 

出 版 物：《International Journal of Biomathematics》 (生物数学学报（英文版）)

年 卷 期：2018年第11卷第6期

页      面：31-57页

核心收录：

学科分类：081704[工学-应用化学] 07[理学] 08[工学] 0817[工学-化学工程与技术] 070305[理学-高分子化学与物理] 080501[工学-材料物理与化学] 0805[工学-材料科学与工程（可授工学、理学学位）] 0703[理学-化学] 081202[工学-计算机软件与理论] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

主　　题：Mathematical model reproductive number next generation matrix method stability analysis Griinwald-Letnikov method numerical simulation. 

摘      要：In this paper, we develop a fractional-order smoking model by considering relapse class. First, we formulate the model and find the unique positive solution for the proposed model. Then we apply the Griinwald-Letnikov approximation in the place of maintaining a general quadrature formula approach to the Riemann-Liouville integral definition of the fractional derivative. Building on this foundation avoids the need for domain trans-formations, contour integration or involved theory to compute accurate approximate solutions of fractional-order giving up smoking model A comparative study between Griinwald-Letnikov method and Runge-Kutta method is presented in the case of integer-order derivative. Finally, we present the obtained results graphically.