Numerical analysis of coupled fractional differential equations with Atangana-Baleanu fractional derivative

Ilknur Koca

doi:10.3934/dcdss.2019031

Article Contents

2019, Volume 12, Issue 3: 475-486. Doi: 10.3934/dcdss.2019031

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Numerical analysis of coupled fractional differential equations with Atangana-Baleanu fractional derivative

Ilknur Koca

Mehmet Akif Ersoy University, Department of Mathematics, Faculty of Sciences, 15100, Burdur, Turkey

Received: June 2017

Revised: September 2017

Published: October 2018

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Abstract

A nonlinear system of two fractional nonlinear differential equations with Atangana-Baleanu derivative is considered in this work. General conditions under which a system solution exists and unique are presented using the fixed-point theorem method. The well-established numerical scheme is used to solve the system of equations. A numerical analysis is presented to secure the stability and convergence of the used numerical scheme.

Keywords:

Non-linear equations,
existence and uniqueness,
Atangana-Baleanu fractional differentiation,
numerical analysis.

Mathematics Subject Classification: Primary: 34A34, 34A12, 34A08; Secondary: 47N40.

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References

	A. A. M. Arafa , S. Z. Rida and H. Mohamed , Homotopy analysis method for solving biological population model, Communications in Theoretical Physics, 56 (2011) , 797-800. doi: 10.1088/0253-6102/56/5/01.
	A. Atangana and D. Baleanu , New fractional derivatives with nonlocal and non-singular kernel: Theory and application to heat transfer model, Thermal Science, 20 (2016) , 763-769. doi: 10.2298/TSCI160111018A.
	A. Atangana and I. Koca , Chaos in a simple nonlinear system with Atangana-Baleanu derivatives with fractional order, Chaos Solitons Fractals, 89 (2016) , 447-454. doi: 10.1016/j.chaos.2016.02.012.
	A. Atangana and I. Koca , On the new fractional derivative and application to Nonlinear Baggs and Freedman model, Journal of Nonlinear Sciences and Applications, 9 (2016) , 2467-2480. doi: 10.22436/jnsa.009.05.46.
	A. Atangana , On the new fractional derivative and application to nonlinear fisher's reaction-diffusion equation, Appl Math Comput, 273 (2016) , 948-956. doi: 10.1016/j.amc.2015.10.021.
	M. Caputo and M. Fabrizio , A new definition of fractional derivative without singular kernel, Progr. Fract. Differ. Appl., 1 (2015) , 73-85.
	A. M. A. El-Sayed , A. Elsaid , I. L. El-Kalla and D. Hammad , A homotopy perturbation technique for solving partial differential equations of fractional order in finite domains, Applied Mathematics and Computation, 218 (2012) , 8329-8340. doi: 10.1016/j.amc.2012.01.057.
	A. K. Golmankhaneh , A. K. Golmankhaneh and D. Baleanu , On nonlinear fractional KleinGordon equation, Signal Processing, 91 (2011) , 446-451.
	A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, 204, Elsevier Science B. V., Amsterdam, 2006.
	J. Losada and J. J. Nieto , Properties of a new fractional derivative without singular kernel, Progr Fract Differ Appl, 1 (2015) , 87-92.
	I. Podlubny , Geometric and physical interpretation of fractional integration and fractional differentiation, Fractional Calculus and Applied Analysis, 5 (2002) , 367-386.
	B. Sambandham and A. Vatsala , Basic results for sequential caputo fractional differential equations, Mathematics, 3 (2015) , 76-91.
	T. Yamamoto and X. Chen , An existence and nonexistence theorem for solutions of nonlinear systems and its application to algebraic equations, Journal of Computational and Applied Mathematics, 30 (1990) , 87-97. doi: 10.1016/0377-0427(90)90008-N.