Positive solutions and stability of fuzzy Atangana–Baleanu variable fractional differential equation model for a novel coronavirus (COVID-19)

作     者：Pratibha Verma Manoj Kumar 

作者机构：Department of Mathematics Motilal Nehru National Institute of Technology Allahabad Prayagraj 211004Uttar PradeshIndia 

出 版 物：《International Journal of Modeling, Simulation, and Scientific Computing》 (建模、仿真和科学计算国际期刊（英文）)

年 卷 期：2021年第12卷第6期

页      面：205-229页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Novel coronavirus(COVID-19) variable Atangana–Baleanu fractional derivative Mittag–Leffler kernel existence and uniqueness fixed point theorems Hyers–Ulam stability 

摘      要：This work provides a new fuzzy variable fractional COVID-19 model and uses a variablefractional operator, namely, the fuzzy variable Atangana–Baleanu fractional derivativesin the Caputo sense. Next, we explore the proposed fuzzy variable fractional COVID-19 model using the fixed point theory approach and determine the solution’s existenceand uniqueness conditions. We choose an appropriate mapping and with the help ofthe upper/lower solutions method. We prove the existence of a positive solution for theproposed fuzzy variable fractional COVID-19 model and also obtain the result on theexistence of a unique positive solution. Moreover, we discuss the generalized Hyers–Ulam stability and generalized Hyers–Ulam–Rassias stability. Further, we investigate theresults on maximum and minimum solutions for the fuzzy variable fractional COVID-19model.