Generalized Gronwall inequalities and their applications to fractional differential equations

By Shi-you Lin. 2013

48 citations recorded by the source corpus.

In this paper, we provide several generalizations of the Gronwall inequality and present their applications to prove the uniqueness of solutions for fractional differential equations with various derivatives.MSC:26A33, 34A08.

Subfields: Applied Mathematics, Mechanics of Materials, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/4782523bdba6aa254a641b7c716562f03deb383f

How researchers see this paper

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In Applied Mathematics

1. Ricardo Almeida
2. Fernando Manuel Ferreira Lobo Pereira
3. H. Ali
4. Sílvio M. A. Gama
5. Fahd Jarad
6. E. Capelas de Oliveira
7. J. Sousa
8. J. Machado

In Mechanics of Materials

1. Ricardo Almeida
2. Fernando Manuel Ferreira Lobo Pereira
3. H. Ali
4. Sílvio M. A. Gama

In Modeling and Simulation

1. Ricardo Almeida
2. Fernando Manuel Ferreira Lobo Pereira
3. H. Ali
4. Sílvio M. A. Gama
5. Fahd Jarad
6. E. Capelas de Oliveira
7. J. Sousa
8. J. Machado

Citations in the corpus

• A Gronwall inequality for a general Caputo fractional operator (2017, methodology): “To end, in Section 4, we present and prove a fractional Gronwall inequality type, generalizing the ones presented in [19, 25, 31].”
• A survey of useful inequalities in fractional calculus (2017, unknown): “Lin [34] obtained the following result.”
• Existence and Ulam stability for nonlinear implicit fractional differential equations with Hadamard derivative (2017, unknown): “([29]) For any t ∈ [1, T ], u(t) ≤ a(t) + b(t) ∫ t”
• A new approach to the Pontryagin maximum principle for nonlinear fractional optimal control problems (2015, methodology): “Here, we will consider the following /epsiintegral extracted from [16].”