J. Appl. Math. Comput.
Monotone iterative technique for a coupled system of
nonlinear Hadamard fractional differential equations
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
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 the Key Scientiﬁc Research Programmes of Higher Education of Henan
Province-Guidance Plan (No. 16B110011).
School of Mathematics, Southeast University, Nanjing 210096, China
Department of Public Education, Sanmenxia Polytechnic, Sanmenxia 472000, China