Comparing the new fractional derivative operators involving exponential and Mittag-Leffler kernel
By Mehmet Yavuz, Necati Özdemir. Discrete and Continuous Dynamical Systems. Series A, 2020
71 citations recorded by the source corpus.
In this manuscript, we have proposed a comparison based on newly defined fractional derivative operators which are called as Caputo-Fabrizio (CF) and Atangana-Baleanu (AB). In 2015, Caputo and Fabrizio established a new fractional operator by using exponential kernel. After one year, Atangana and Baleanu recommended a different-type fractional operator that uses the generalized Mittag-Leffler function (MLF). Many real-life problems can be modelled and can be solved by numerical-analytical solution methods which are derived with these operators. In this paper, we suggest an approximate solution method for PDEs of fractional order by using the mentioned operators. We consider the Laplace homotopy transformation method (LHTM) which is the combination of standard homotopy technique (SHT) and Laplace transformation method (LTM). In this study, we aim to demonstrate the effectiveness of the aforementioned method by comparing the solutions we have achieved with the exact solutions. 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/0b1ee7ae0405cc22707fc505e8cfdb7075e1c94f
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Citations in the corpus
- Characterizations of two different fractional operators without singular kernel (2019, methodology): “In this paper, the mentioned LHTM for numerical-approximate solutions of FPDEs is considered.”
- Analysis and numerical computations of the fractional regularized long‐wave equation with damping term (2020, unknown): “It implies that ||φ1(ξ, ζ ) − φ2(ξ, ζ )|| = 0, (39) which gives φ1(ξ, ζ ) = φ2(ξ, ζ ).”