Numerical solutions and geometric attractors of a fractional model of the cancer-immune based on the Atangana-Baleanu-Caputo derivative and the reproducing kernel scheme

Abstract

• This paper discusses a mathematical model that aims to investigate the interaction between the IS and CCs by incorporating ℐℒ − 12 cytokine together with an anti- P D − L 1 inhibitor. • The utilized fractional differential problem is a modern mathematical formation model evaluated by the reproducing Hilbert scheme used with the fractional Atangana-Baleanu-Caputo derivative. • The required Hilbert spaces were included, and the representation theory of the solutions was presented together with several related results. • Some mathematical analyses like error convergence analysis, attitude, and its order degree were also included. • Novel steps are fitted for the covering fractional model to gain its numeric-analytic solutions. • Several plots and tables were presented and discussed to illustrate the mathematical and physiological behavior of this disease, in addition to the effect of the degree of fractional derivatives used in it. • The summary of the presented work and various scientific recommendations in addition to the future work that complements this work has been utilized in the last part Recently, it has become critical to attempt to recognize diseases with high death rates around the world like infectious diseases and cancer. As a result, modeling in mathematics may be utilized to give feedback on diseases that enabled influence every one of us. This paper discusses a mathematical model that aims to investigate the interaction between the IS and CCs by incorporating I L − 12 cytokine together with an anti- P D − L 1 inhibitor. The utilized fractional differential problem is a modern mathematical formation model evaluated by the reproducing Hilbert scheme used with the fractional Atangana-Baleanu-Caputo derivative. The required Hilbert spaces were included, and the representation theory of the solutions was presented together with several related results. Some mathematical analyses like error attitude and its order degree were also included. To illustrate the mathematical and physiological behavior of this disease, several plots and tables were presented and discussed, in addition to the effect of the degree of fractional derivatives used in it. The summary of the presented work and various scientific recommendations in addition to the future work that complements this work has been utilized in the last part.