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

Khadidja Nisse and Lamine Nisse
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Khadidja Nisse: Department of Mathematics, Faculty of Exact Sciences, Echahide Hamma Lakhdar University, B.P. 789, El Oued 39000, Algeria
Lamine Nisse: Department of Mathematics, Faculty of Exact Sciences, Echahide Hamma Lakhdar University, B.P. 789, El Oued 39000, Algeria

Mathematics, 2017, vol. 6, issue 1, 1-13

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.

Keywords: functional differential equations; fractional calculus; iterative procedures (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2017
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