Existence results for fractional order functional differential equations with infinite delay

By Mouffak Benchohra, J. Henderson, Sotiris K. Ntouyas, Abdelghani Ouahab. 2008

564 citations recorded by the source corpus.

The Banach fixed point theorem and the nonlinear alternative of Leray–Schauder type are used to investigate the existence of solutions for fractional order functional and neutral functional differential equations with infinite delay.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/ed228b56fa14b93d0bcb754e8cca100788bd8fa5

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In Applied Mathematics

1. Ravi P. Agarwal
2. Jinrong Wang
3. Yong Zhou
4. Bashir Ahmad
5. Mouffak Benchohra
6. J. J. Nieto
7. S. Hamani
8. Fulai Chen

In Modeling and Simulation

1. Yong Zhou
2. Bashir Ahmad
3. Ravi P. Agarwal
4. Jinrong Wang
5. Mouffak Benchohra
6. J. J. Nieto
7. N. Kosmatov
8. Fulai Chen

In Numerical Analysis

1. Ravi P. Agarwal
2. Bashir Ahmad
3. Mouffak Benchohra
4. J. J. Nieto
5. N. Kosmatov
6. Rathinasamy Sakthivel
7. S. Hamani
8. Fulai Chen

Citations in the corpus

• On the Application of Measure of Noncompactness to the Existence of Solutions for Fractional Differential Equations (2009, background): “In cause, in part to the intensive development of the theory of fractional calculus itself, we refer the reader to the papers of Agarwal et al. [1, 2], Belarbi et al. [13], Benchohra et al. [14, 15 ], Delboso and Rodino [16], Diethelm and Ford [17], El-Sayed et al. [18], Kilbas and Marzan [23] and ”
• A boundary value problem of fractional order at resonance. (2010, background): “$ I t w i l l be shown that , with the pre sent \noindent cho i c e o f boundary c o n d i t i o n s , the boundary value problem i s at resonance .”
• Well-posedness and numerical algorithm for the tempered fractional differential equations (2019, background): “For the global existence and uniform asymptotic stability results of fractional functional differential equations corresponding to (23), one can see [27, 3].”
• 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”
• IMPULSIVE FRACTIONAL DIFFERENTIAL EQUATIONS IN BANACH SPACES (2009, unknown): “[12, 13, 15], Delboso and Rodino [20], Diethelm and Ford [22], El-Sayed et al.”
• A singular boundary value problem for nonlinear differential equations of fractional order (2009, background): “For only several among numerous advances in the theory and applications of differential equations of fractional order, we refer the reader to [3–7, 11, 15, 16, 20] and the references therein.”