Uniqueness results for fractional functional differential equations with infinite delay in Fréchet spaces

By Abdelkader Belarbi, Mouffak Benchohra, Abdelghani Ouahab. 2006

98 citations recorded by the source corpus.

In this article, a recent nonlinear alternative for contraction maps in Fréchet spaces due to Frigon and Granas [1998, Résultats de type Leray-Schauder pour des contractions sur des espaces de Fréchet, Ann. Sci. Math. Québec 22, 161–168] is used to investigate the existence and uniqueness of solutions for fractional order functional differential equations with infinite delay.

Subfields: Applied Mathematics, Control and Systems Engineering, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/2dae8e088f7992ffa845ccb3bd6333f8860b233e

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In Applied Mathematics

In Control and Systems Engineering

In Modeling and Simulation

Citations in the corpus

A Survey on Existence Results for Boundary Value Problems of Nonlinear Fractional Differential Equations and Inclusions (2010, background): “In [ 15 , 28] the authors studied the existence and uniqueness of solutions of classes of initial value problems for functional differential equations with infinite delay and fractional order, and in [16] a class of perturbed functional differential equations involving the Caputo fractional derivati”
Existence results for boundary value problems with non-linear fractional differential equations (2008, background): “In [28,29], the authors studied the existence and uniqueness of solutions of classes of initial value problems for functional differential equations with infinite delay and fractional order; in [30], a class of perturbed functional differential equations involving the Caputo fractional derivative wa”
Positive solutions of a boundary value problem for a nonlinear fractional differential equation. (2008, unknown): “While much attention has focused on the Cauchy problem for fractional differential equations for both the Reimann-Liouville and Caputo differential operators, see [8, 17, 24, 28, 29, 30, 31, 32, 34] and references therein, there are few papers devoted to the study of fractional order boundary value ”
Existence results for boundary-value problems with nonlinear fractional differential inclusions and integral conditions. (2010, background): “In [7, 12] the authors studied the existence and uniqueness of solutions of classes of initial value problems for functional differential equations with infinite delay and fractional order, and in [6] a class of perturbed functional differential equations involving the Caputo fractional derivative h”
On fractional order derivatives and Darboux problem for implicit differential equations (2012, unknown): “[4], Benchohra et al.”
The existence and uniqueness of mild solutions for impulsive fractional equations with nonlocal conditions and infinite delay (2010, background): “For details, see [1–8] and the references therein.”
Boundary Value Problems for Differential Equations Involving Riemann-Liouville Fractional Derivative on the Half-Line (2011, background): “In [7, 8] the authors studied the existence and uniqueness of solutions of classes of initial value problems for functional differential equations with infinite delay and fractional order, and in [6] a class of perturbed functional differential equations involving the Caputo fractional derivative ha”
Boundary Value Problems for Fractional Differential Equations (2009, background): “In a series of papers (see [1, 2, 3]) the authors considered some classes of initial value problems for functional differential equations involving Riemann–Liouville and Caputo fractional derivatives of order 0 < α ≤ 1.”