Fractal-fractional order dynamics and numerical simulations of a Zika epidemic model with insecticide-treated nets

Fractional order epidemiological model of SARS-CoV-2 dynamism involving Alzheimer’s disease

“…Stability is one of crucial component of differential equation. There has been many stability-type concepts that study dynamical systems, the HU stability-type concept has recently used for many epidemiological models, due to the approximation properties in the solutions which reduce the burden of getting exact solutions, for example (see [52] ) and references therein. To assess and analyse the SARS-CoV-2 transmission model incorporating Alzheimer’s disease, we apply the concept of HU stability-type to get approximate solution for our proposed model.…”

A fractional order Monkeypox model with protected travelers using the fixed point theorem and Newton polynomial interpolation

“…This form of stability can be helpful when dealing with a wide array of natural occurrences for which it is difficult to find an exact or precise solution. In the epidemiological model, where it might be challenging to acquire an exact solution at times, the HU stability component is used to get an approximation solution in order to manage the dynamism of a set of fractional equations [39] . To obtain the global stability of the equilibrium points, we use the Ulam-Hyers stability criteria.…”

“…When a derivative has a non-fixed order, it gives a better picture of real-world problems. Fractional calculus, which is defined as the extension or generalization of classical derivatives and integrals to non-integer order situations, has received a lot of academic interest in recent years and appear to be powerful mathematical tools to model complex real world problems in a variety of domains, such as epidemiological models, image processing, chaos theory, and so on (see, [35] , [36] , [37] , [38] , [39] , [40] ). New approaches concerning fractional operators, such as the exponential decay and the Mittag-Leffler kernel, have been proposed in recent years.…”

Multiple positive solutions and stability results for nonlinear fractional delay differential equations involving p ‐Laplacian operator

“…This is because the dynamic transmissions that take place in biological models can be accurately modeled using fractional calculus (see for example, Mohammadi et al [14], Etemad et al [15], Baleanu et al [16], Tuan et al [17], Addai et al [18]).The fractional calculus has improved the modeling precision of many phenomena in the physical sciences. Primarily, Caputo fractional derivative, the Caputo–Fabrizio (CF) derivative, and Atangana–Baleanu–Caputo (ABC) have lately been used in the field of mathematical biology (see, for example, previous works [19–23] and the references therein).…”