New numerical approach for fractional differential equations

• Published in: Mathematical modelling of natural phenomena Vol. 13; no. 1; p. 3
• Main Authors: Atangana, Abdon, Owolabi, Kolade M.
• Format: Journal Article
• Language: English
• Published: Les Ulis EDP Sciences 2018
• Subjects: 26A33; 34A34; 35B44; 65M06; Adams-Bashforth method; Atangana-Baleanu derivative; Caputo-Fabrizio derivative; Differential equations; fractional differential equation; Kernels; Nonlinear systems; Nonlinearity; numerical approximation; Power law

In the present case, we propose the correct version of the fractional Adams-Bashforth methods which take into account the nonlinearity of the kernels including the power law for the Riemann-Liouville type, the exponential decay law for the Caputo-Fabrizio case and the Mittag-Leffler law for the Atan...