Theoretical and semi-analytical results to a biological model under Atangana–Baleanu–Caputo fractional derivative

Advances in Difference Equations

article

Zeb, Anwar¹  Nazir, Ghazala²  Shah, Kamal²  Alzahrani, Ebraheem³ 

[1] Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus;Department of Mathematics, University of Malakand;Department of Mathematics, Faculty of Science, King Abdulaziz University

关键词: Fractional order differential equation;    Atangana–Baleanu–Caputo fractional derivative;    Laplace Adomian decomposition method;    SIR model;   

DOI  :  10.1186/s13662-020-03117-7

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

This manuscript is related to finding a solution of the SIR model under Mittag-Leffler type derivative. For the required results, we use Laplace transform together with Adomian decomposition method (LADM). The mentioned method is a powerful tool to deal with various linear and nonlinear problems of “fractional order differential equations (FODEs)”. Also, we study some results devoted to qualitative theory for the concerned model. Computational results show the verification of the established analysis. Briefly, we state that qualitative theory for the existence of solution is important to ensure whether the considered problem has a solution or not. Further ensuring the existence of solution, we investigate approximate solution which is computed in the form of infinite series. The results are graphically displayed to analyze the adopted procedure for solving nonlinear FODEs under ABC derivative.

【 授权许可】

CC BY