Abstract
Abstract A work on a mathematical modeling is very popular in applied sciences. Nowadays many mathematical models have been considered and new methods have been used for approaching of these models. In this paper we are considering mathematical modeling of nuclear family model with fractional order Caputo derivative. Also the existence and uniqueness results and numerical scheme are given with Adams-Bashforth scheme via fractional order Caputo derivative.
Highlights
New efficient numerical methods have been developed for solutions of differential equations with different definitions of derivatives
In this work we are interesting in mathematical modeling of nuclear family
Model was introduced by Koca in 2015 with Caputo type fractional derivative [1]
Summary
New efficient numerical methods have been developed for solutions of differential equations with different definitions of derivatives. For example the kernels including the power law for the Riemann-Liouville and Caputo type, the exponential decay law for the Caputo-Fabrizio case and the Mittag-Leffler law for the Atangana-Baleanu derivative [2,3,4,5,6, 11,12,13,14]. Ilknur Koca and Pelin Yaprakdal Applied Mathematics and Nonlinear Sciences 5(2020) 393–404 and Batogna have extended this method for partial differential equation with Caputo-Fabrizio derivative [10] in their thesis. Owolabi and Atangana formulated a new three-step fractional Adams-Bashforth scheme with Caputo-Fabrizio derivative [7,8,9]. In numerical part; we consider the solutions of system with two-step AdamsBashforth scheme via fractional order Caputo derivative
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