Modeling and numerical investigation of fractional‐order bovine babesiosis disease

• Published in: Numerical methods for partial differential equations 2021-05, Vol.37 (3), p.1946-1964
• Main Authors: Ahmad, Aqeel, Farman, Muhammad, Naik, Parvaiz Ahmad, Zafar, Nayab, Akgul, Ali, Saleem, Muhammad Umer
• Format: Article
• Language: English
• Subjects: ABC fractional‐order derivative; bovine babesiosis; Caputo fractional derivative; Differential equations; Exact solutions; Existence theorems; Fractional calculus; Iterative methods; Laplace transforms; mathematical model; Mathematical models; Polynomials; Populations
• ISSN: 0749-159X; 1098-2426
• DOI: 10.1002/num.22632

In this paper, analysis and modeling of bovine babesiosis disease are designed with fractional calculus. The solution for a bovine babesiosis disease and tick populations fractional order system is determined using the Caputo and Atangana–Baleanu–Caputo (ABC) fractional derivatives. Applying the homotopy analysis method and the Laplace transform with polynomial homotopy, the analytical solution of the bovine babesiosis disease has obtained. Furthermore, using an iterative scheme by the Laplace transform, and the Atangana–Baleanu fractional integral, special solutions of the model are obtained. Uniqueness and existence of the solutions by the fixed‐point theorem and Picard–Lindel of approach are studied. Numerical simulation has been established for both Caputo and ABC fractional derivative of the proposed system is carried out. The numeric replications for diverse consequences are carried out, and data attained are in good agreement with theoretical outcomes, displaying a vital perception about the use of the set of fractional coupled differential equations to model babesiosis disease and tick populations.