New numerical approach for fractional differential equations

By Abdon Atangana, Kolade M. Owolabi. 2017

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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 Atangana-Baleanu scenario. The Adams-Bashforth method for fractional differentiation suggested and are commonly use in the literature nowadays is not mathematically correct and the method was derived without taking into account the nonlinearity of the power law kernel. Unlike the proposed version found in the literature, our approximation, in all the cases, we are able to recover the standard case whenever the fractional power $\alpha=1$.

Subfields: Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/8ed04ad2d6ca54f95650932cc54c2481e7456313

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Citations in the corpus

Numerical investigations on COVID‐19 model through singular and non‐singular fractional operators (2020, methodology): “Several numerical techniques have been suggested to solve the arbitrary-order differential equations (DEs) [2, 6, 8, 11, 16].”