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Modeling and numerical investigation of fractional‐order bovine babesiosis disease
Author(s) -
Ahmad Aqeel,
Farman Muhammad,
Naik Parvaiz Ahmad,
Zafar Nayab,
Akgul Ali,
Saleem Muhammad Umer
Publication year - 2021
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22632
Subject(s) - mathematics , fractional calculus , uniqueness , laplace transform , babesiosis , fixed point theorem , mathematical analysis , veterinary medicine , medicine
Abstract 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.