Nonlinear fractional mathematical model of tuberculosis (TB) disease with incomplete treatment under Atangana-Baleanu derivative

Abstract

The current work investigates the mathematical model of Tuberculosis disease with incomplete treatment under the Atangana-Baleanu-Caputo (ABC) derivative with fractional order. Upon exploiting fixed point approach and nonlinear analysis, we derive some theoretical results about solution existence and its stability. The famous fractional Adam Bashforth technique is applied to compute numerical solution to the considered model. The aforesaid tool is based on fundamental theorem of fractional calculus and Lagrange interpolation polynomials. Additionally, various numerical plots are given corresponding to different fractional order in (0,1].

Keywords

• Tuberculosis disease model
• Atangana-Baleanu derivative
• Existence and uniqueness
• Fractional Adams-Bashforth method