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Shi, A.L. and Zhang, S.Q. (2009) Upper and Lower Solutions Method and a Fractional Differential Equation Boundary Value Problem. Electronic Journal of Qualitative Theory of Differential Equations, 2009, 1-13.
https://doi.org/10.14232/ejqtde.2009.1.30

has been cited by the following article:

• TITLE: Mixed Monotone Iterative Technique for Singular Hadamard Fractional Integro-Differential Equations in Banach Spaces

  AUTHORS: Xinwei Su, Shuqin Zhang, Yu Hui

  KEYWORDS: Hadamard Fractional Derivative, Nonlinear Boundary Condition, Monotone Iterative Technique, Noncompactness Measure

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.10 No.12, December 30, 2022

  ABSTRACT: This paper deals with fractional integro-differential equations involving Hadamard fractional derivatives and nonlinear boundary conditions in an ordered Banach space. The nonlinearity is allowed to be singular with respect to time variable. Under some monotonicity conditions and noncompactness measure conditions, we use the method of coupled lower and upper L-quasisolutions associated with the mixed monotone iterative technique to investigate the existence of extremal L-quasisolutions. A unique solution between coupled lower and upper L-quasisolutions is also obtained. An example is given to illustrate our theoretical results. The results got in this paper are new and enrich the existing related work.