Ulam-Hyers stability of tuberculosis and COVID-19 co-infection model under Atangana-Baleanu fractal-fractional operator

Abstract

The intention of this work is to study a mathematical model for fractal-fractional tuberculosis and COVID-19 co-infection under the Atangana-Baleanu fractal-fractional operator. Firstly, we formulate the tuberculosis and COVID-19 co-infection model by considering the tuberculosis recovery individuals, the COVID-19 recovery individuals, and both disease recovery compartment in the proposed model. The fixed point approach is utilized to explore the existence and uniqueness of the solution in the suggested model. The stability analysis related to solve the Ulam-Hyers stability is also investigated. This paper is based on Lagrange’s interpolation polynomial in the numerical scheme, which is validated through a specific case with a comparative numerical analysis for different values of the fractional and fractal orders.

Mathematical Identification Analysis of a Fractional-Order Delayed Model for Tuberculosis

“…In the real world, however, we do not know the "fair" values of the parameters, so we cannot directly assess the quality of their recovery. This is why we introduced the residual measure Equation (21). If the solution to the direct problems with the implied parameters mimics the observed dynamics, we can be confident in the parameter estimates.…”

“…In the study of [21], a mathematical model was studied for the co-infection of tuberculosis and COVID-19 using the Atangana-Baleanu fractal-fractional operator, considering compartments for recovery from both diseases. They confirmed the existence and uniqueness of a model solution through a fixed-point approach, investigated the Ulam-Hyers stability, and validated the model using Lagrange interpolation polynomial in a numerical scheme, comparing different values of fractional and fractal orders.…”

Oceanic Shallow-Water Investigations on a Variable-Coefficient Davey–Stewartson System

“…The solutions and properties of differential equations are significant [1,2]. For example, the stability of a differential equation not only reflects the characteristics of the equation itself, it plays a role in practical model analysis [3][4][5][6]. Differential equations can be divided into linear equations and nonlinear equations.…”

Ulam–Hyers Stability of Linear Differential Equation with General Transform

“…The new approaches and techniques developed in the field of Ulam-Hyers stability in differential equations find a lot of applications in other areas such as physics, electronics, biology, economics, mechanics, etc. [5][6][7]. The stability of functional equations is studied in [8] and the application of parallel electrical circuits.…”