78 research outputs found
Monotone iterative procedure and systems of a finite number of nonlinear fractional differential equations
The aim of the paper is to present a nontrivial and natural extension of the
comparison result and the monotone iterative procedure based on upper and lower
solutions, which were recently established in (Wang et al. in Appl. Math. Lett.
25:1019-1024, 2012), to the case of any finite number of nonlinear fractional
differential equations.The author is very grateful to the reviewers for the remarks, which improved the final version of the manuscript. This
article was financially supported by University of Łódź as a part of donation for the research activities aimed at the
development of young scientists, grant no. 545/1117
Jacobi-Predictor-Corrector Approach for the Fractional Ordinary Differential Equations
We present a novel numerical method, called {\tt Jacobi-predictor-corrector
approach}, for the numerical solution of fractional ordinary differential
equations based on the polynomial interpolation and the Gauss-Lobatto
quadrature w.r.t. the Jacobi-weight function
. This method has the computational cost
O(N) and the convergent order , where and are, respectively, the
total computational steps and the number of used interpolating points. The
detailed error analysis is performed, and the extensive numerical experiments
confirm the theoretical results and show the robustness of this method.Comment: 24 pages, 5 figure
Nonlinear fractional differential equations in nonreflexive Banach spaces and fractional calculus
The aim of this paper is to correct some ambiguities and inaccuracies in Agarwal et al. (Commun. Nonlinear Sci. Numer. Simul. 20(1): 59-73, 2015; Adv. Differ. Equ. 2013: 302, 2013, doi:10.1186/1687-1847-2013-302) and to present new ideas and approaches for fractional calculus and fractional differential equations in nonreflexive Banach spaces
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