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Monotone domain decomposition iterative technique for boundary value problems of a nonlinear fractional differential equation

Myong-Gil Rim

Faculty of Mathematics, Kim Il Sung University, Pyongyang, Democratic People’s Republic of Korea

E-mail Address: ryongnam16@yahoo.com

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and

Chol-Guk Choe

Faculty of Mathematics, Kim Il Sung University, Pyongyang, Democratic People’s Republic of Korea

E-mail Address: ryongnam30@yahoo.com

Corresponding author.

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https://doi.org/10.1142/S1793557119500116Cited by:0 (Source: Crossref)

Abstract

In this paper, we present a monotone domain decomposition iterative technique for boundary value problems of a nonlinear fractional differential equation. We construct two monotone domain decomposition sequences of upper and lower solutions which converge uniformly to the actual solution of the problem. The accuracy and efficiency of our new approach are demonstrated through two examples.

Communicated by B.-W. Schulze

Keywords:

AMSC: 34A08, 32G34

References

1. M. Al-Refai and M. Ali Hajji, Monotone iterative sequences for nonlinear boundary value problems of fractional order, Nonlinear Anal. 74 (2011) 3531–3539. Crossref, Web of Science, Google Scholar
2. R. Darzi, B. Mohammadzadeh and A. Neamaty, Lower and upper solutions method for positive solutions of fractional boundary value problems, Abstr. Appl. Anal. (2013). Crossref, Google Scholar
3. C. Hu, B. Liu and S. Xie, Monotone iterative solutions for non-linear boundary value problems of fractional differential equation, Abstr. Appl. Anal. (2013). Crossref, Google Scholar
4. A. A. Kilbas, H. M. Srivastava and J. J. Trujjllo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, Vol. 204 (Elsevier, Amsterdam, 2006). Google Scholar
5. G. Wang, Monotone iterative technique for boundary value problems of a nonlinear fractional differential equation with deviating arguments, J. Comput. Appl. Math. 236 (2012) 2425–2430. Crossref, Web of Science, Google Scholar