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

ABSTRACT

This work provides a new fuzzy variable fractional COVID-19 model and uses a variable fractional operator, namely, the fuzzy variable Atangana-Baleanu fractional derivatives in 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 existence and uniqueness conditions. We choose an appropriate mapping and with the help of the upper/lower solutions method. We prove the existence of a positive solution for the proposed fuzzy variable fractional COVID-19 model and also obtain the result on the existence of a unique positive solution. Moreover, we discuss the generalized Hyers-Ulam stability and generalized Hyers-Ulam-Rassias stability. Further, we investigate the results on maximum and minimum solutions for the fuzzy variable fractional COVID-19 model. © 2021 World Scientific Publishing Company.