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Mathematics 2018, 6(1), 2; doi:10.3390/math6010002

An Iterative Method for Solving a Class of Fractional Functional Differential Equations with “Maxima”

1
Department of Mathematics, Faculty of Exact Sciences, Echahide Hamma Lakhdar University, B.P. 789, El Oued 39000, Algeria
2
Laboratory of Applied Mathematics, Badji Mokhtar University, B.P. 12, Annaba 23000, Algeria
*
Author to whom correspondence should be addressed.
Received: 14 November 2017 / Revised: 16 December 2017 / Accepted: 19 December 2017 / Published: 22 December 2017
(This article belongs to the Special Issue Fractional Calculus: Theory and Applications)
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Abstract

In the present work, we deal with nonlinear fractional differential equations with “maxima” and deviating arguments. The nonlinear part of the problem under consideration depends on the maximum values of the unknown function taken in time-dependent intervals. Proceeding by an iterative approach, we obtain the existence and uniqueness of the solution, in a context that does not fit within the framework of fixed point theory methods for the self-mappings, frequently used in the study of such problems. An example illustrating our main result is also given. View Full-Text
Keywords: functional differential equations; fractional calculus; iterative procedures functional differential equations; fractional calculus; iterative procedures
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Nisse, K.; Nisse, L. An Iterative Method for Solving a Class of Fractional Functional Differential Equations with “Maxima”. Mathematics 2018, 6, 2.

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