On the new fractional derivative and application to nonlinear Baggs and Freedman model

Volume 9, Issue 5, pp 2467--2480 http://dx.doi.org/10.22436/jnsa.009.05.46

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Authors

Abdon Atangana - Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, 9300, Bloemfontein, South Africa. Ilknur Koca - Department of Mathematics, Faculty of Sciences, Mehmet Akif Ersoy University, 15100, Burdur, Turkey.

Abstract

We presented the nonlinear Baggs and Freedman model with new fractional derivative. We derived the special solution using an iterative method. The stability of the iterative method was presented using the fixed point theory. The uniqueness of the special solution was presented in detail using some properties of the inner product and the Hilbert space. We presented some numerical simulations to underpin the effectiveness of the used derivative and semi-analytical method.

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Keywords

• Nonlinear Baggs and Freedman model
• special solution
• fixed point theorem
• iterative method.

MSC

•  34A34
•  47H10
•  65L07

References

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