Smoothness and stability of the solutions for nonlinear fractional differential equations

By Weihua Deng. 2010

158 citations recorded by the source corpus.

This paper first obtains the differentiability properties of the solutions for nonlinear fractional differential equations, and then the sufficient conditions for the local asymptotical stability of nonlinear fractional differential equations are also derived.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/9e6b75234e4b2f20e48f6cab52bf79ce23bf2826

How researchers see this paper

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In Applied Mathematics

1. Fulai Chen
2. Da-Xue Chen
3. Yong Zhou
4. Yi Chai
5. Yigang He
6. Liping Chen
7. Y. Lan
8. R. Wu

In Modeling and Simulation

1. Fulai Chen
2. Da-Xue Chen
3. Yong Zhou
4. Yi Chai
5. Yigang He
6. Liping Chen
7. Y. Lan
8. R. Wu

In Numerical Analysis

1. Fulai Chen
2. Yi Chai
3. Yong Zhou
4. Yigang He
5. Liping Chen
6. Y. Lan
7. Da-Xue Chen
8. R. Wu

Citations in the corpus

• OSCILLATORY BEHAVIOR OF A CLASS OF FRACTIONAL DIFFERENTIAL EQUATIONS WITH DAMPING (2013, methodology): “Many papers have investigated some aspects of fractional differential equations, such as the existence and uniqueness of solutions to Cauchy type problems, the methods for explicit and numerical solutions, and the stability of solutions, and we refer to [12–19].”
• Dα‐Type Iterative Learning Control for Fractional‐Order Linear Time‐Delay Systems (2013, background): “is equivalent to the following nonlinear Volterra integral equation [22]:”
• New results on stability and stabilization of a class of nonlinear fractional-order systems (2013, background): “Deng derived sufficient conditions for the local asymptotical stability of nonlinear fractional-order systems with fractional-order α : 0 < α < 1 [22].”
• Fixed points and asymptotic stability of nonlinear fractional difference equations (2011, background): “Some local asymptotical stability, Mittag-Leffler stability and linear matrix inequality (LMI) stability are discussed in [13, 15, 21, 22, 27], Chen and Zhou [13] considered the attractivity of fractional functional differential equations by Schauder fixed point theorem, Deng [15] discussed the attr”