文章基本信息

标题：Theoretical and semi-analytical results to a biological model under Atangana–Baleanu–Caputo fractional derivative
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作者：Anwar Zeb ; Ghazala Nazir ; Kamal Shah 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2020
卷号：2020
期号：1
页码：1-11
DOI：10.1186/s13662-020-03117-7
出版社：Hindawi Publishing Corporation
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.
关键词：Fractional order differential equation ; Atangana–Baleanu–Caputo fractional derivative ; Laplace Adomian decomposition method ; SIR model