Characterizations of two different fractional operators without singular kernel

By Mehmet Yavuz. Mathematical Modelling of Natural Phenomena, 2019

79 citations recorded by the source corpus.

In this paper, we analyze the behaviours of two different fractional derivative operators defined in the last decade. One of them is defined with the normalized sinc function (NSF) and the other one is defined with the Mittag-Leffler function (MLF). Both of them have a non-singular kernel. The fractional derivative operator defined with the MLF is developed by Atangana and Baleanu (ABO) in 2016 and the other operator defined with the normalized sinc function (NSFDO) is created by Yang et al. in 2017. These mentioned operators have some advantages to model the real life problems and to solve them. On the other hand, since the Laplace transform (LT) of the ABO can be calculated more easily, it can be preferred to solve linear/nonlinear problems. In this study, we use the perturbation method with coupled the LTs of these operators to analyze their performance in solving some fractional differential equations. Furthermore, by constructing the error analysis, we test the practicability and usefulness of the method.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/79107b035b51db5093f3e3d8cd9a4f5ea749c4e6

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In Applied Mathematics

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

Reproducing kernel approach for numerical solutions of fuzzy fractional initial value problems under the Mittag–Leffler kernel differential operator (2021, background): “So x t ð Þ 1⁄2 r in Equation (29) symbolizes the analytic solution of Equation (25).”