# Monotone iterative technique for a coupled system of nonlinear Hadamard fractional differential equations

Monotone iterative technique for a coupled system of nonlinear Hadamard fractional differential... J. Appl. Math. Comput. https://doi.org/10.1007/s12190-018-1192-x ORIGINAL RESEARCH Monotone iterative technique for a coupled system of nonlinear Hadamard fractional differential equations 1,2 Wengui Yang Received: 23 November 2017 © Korean Society for Computational and Applied Mathematics 2018 Abstract In this paper, we investigate the extremal solutions for a coupled system of nonlinear Hadamard fractional differential equations with Cauchy initial value conditions. By using the comparison principle and the monotone iterative technique combined with the method of upper and lower solutions, we obtain the existence and iterative methods of extremal solution to the system. Finally, an example with numerical simulation is given to show the effectiveness of our main results. Keywords Hadamard fractional differential equations · Extremal solutions · Monotone iterative technique · Upper and lower solutions Mathematics Subject Classiﬁcation 34B18 · 26A33 · 34A34 1 Introduction Due to the fact that fractional differential equations can better describe many phe- nomena than ordinary differential equations in many diverse and widespread ﬁelds of science and engineering such as control, porous media, electrochemistry, viscoelas- ticity, electromagnetic, etc., fractional differential equations have given rise to abroad This work was supported by the Scientiﬁc Research Foundation of Graduate School of Southeast University (No. YBJJ1824) and http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Applied Mathematics and Computing Springer Journals

# Monotone iterative technique for a coupled system of nonlinear Hadamard fractional differential equations

, Volume OnlineFirst – Jun 1, 2018
12 pages

Publisher
Springer Berlin Heidelberg
Subject
Mathematics; Computational Mathematics and Numerical Analysis; Mathematical and Computational Engineering; Theory of Computation; Mathematics of Computing
ISSN
1598-5865
eISSN
1865-2085
D.O.I.
10.1007/s12190-018-1192-x
Publisher site
See Article on Publisher Site

### Abstract

J. Appl. Math. Comput. https://doi.org/10.1007/s12190-018-1192-x ORIGINAL RESEARCH Monotone iterative technique for a coupled system of nonlinear Hadamard fractional differential equations 1,2 Wengui Yang Received: 23 November 2017 © Korean Society for Computational and Applied Mathematics 2018 Abstract In this paper, we investigate the extremal solutions for a coupled system of nonlinear Hadamard fractional differential equations with Cauchy initial value conditions. By using the comparison principle and the monotone iterative technique combined with the method of upper and lower solutions, we obtain the existence and iterative methods of extremal solution to the system. Finally, an example with numerical simulation is given to show the effectiveness of our main results. Keywords Hadamard fractional differential equations · Extremal solutions · Monotone iterative technique · Upper and lower solutions Mathematics Subject Classiﬁcation 34B18 · 26A33 · 34A34 1 Introduction Due to the fact that fractional differential equations can better describe many phe- nomena than ordinary differential equations in many diverse and widespread ﬁelds of science and engineering such as control, porous media, electrochemistry, viscoelas- ticity, electromagnetic, etc., fractional differential equations have given rise to abroad This work was supported by the Scientiﬁc Research Foundation of Graduate School of Southeast University (No. YBJJ1824) and

### Journal

Journal of Applied Mathematics and ComputingSpringer Journals

Published: Jun 1, 2018

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