The aim of this paper is to study the dynamics of Dengue disease model using a novel piecewise derivative approach in the sense of singular and non-singular kernels. The singular kernel operator is in the sense of Caputo, whereas the non-singular kernel operator is the Atangana–Baleanu Caputo operator. The existence and uniqueness of a solution with piecewise derivative are examined for the aforementioned problem. The suggested...

Fractional calculus plays an important role in the development of control strategies, the study of the dynamical transmission of diseases, and some other real-life problems nowadays. The time-fractional HIV/AIDS model is examined using a novel method in this paper. Based on the Atangana-concept Baleanu’s of a derivative in the Caputo sense, the current modified fractional derivative operator uses singular and non-local kernels....

A new approach is used to investigate the analytical solutions of the mathematical fractional Casson fluid model that is described by the Constant Proportional Caputo fractional operator having non-local and singular kernel near an infinitely vertical plate. The phenomenon has been expressed in terms of partial differential equations, and the governing equations were then transformed in non-dimensional form. For the sake of generalized...