Theoretical and numerical investigation of a modified ABC fractional operator for the spread of polio under the effect of vaccination

Abstract

The current manuscript investigates a model of the spread of polio under the condition of vaccination by using the novel modified Atangana-Baleanu-Caputo (mABC) fractional derivative. This problem has been studied for non-zero solutions under the modified operator. The series-type solution has been obtained through the application of a Laplace transformation, along with the decomposition technique and Adomian polynomial for the nonlinear terms. The qualitative analysis for the solution of the model has been tested by using fixed point theory. The stability of the solution is also crucial for a dynamical system; therefore, it was checked by using the T-Picard method. With the help of the approximate scheme, numerical simulations were conducted for the proposed model by using different fractional orders and transmission parameters. Based on the obtained positivity of the solutions and numerical stability, we have established the analysis of the mABC operator in the field of fractional calculus and other physical sciences.

Keywords

• modified atangana-baleanu derivative
• qualitative analysis
• laplace adomian decomposition technique
• polio model