UNIQUENESS RESULTS AND CONVERGENCE OF SUCCESSIVE APPROXIMATIONS FOR FRACTIONAL DIFFERENTIAL EQUATIONS

Year 2013, Volume: 42 Issue: 2, 149 - 158, 01.02.2013

Jun Wu Yicheng Liu

Abstract

In this paper, we establish some existence and uniqueness results foran initial value problem with a Caputo fractional derivative. Also, theconvergence of successive approximations is exhibited. Our methodsare based on the equivalent norm techniques and fixed point theorem.

Keywords

Fractional differential equations, Krasnoselskii-Krein type condition, Equivalent norm.

UNIQUENESS RESULTS AND CONVERGENCE OF SUCCESSIVE APPROXIMATIONS FOR FRACTIONAL DIFFERENTIAL EQUATIONS

Abstract

References

• Agarwal, R.P., Zhou, Y., He, Y., Existence of fractional neutral functional differential equations, Computers and Mathematics with Applications, In Press.
• Ahmad, B., Nieto, J.J., Existence of solutions for nonlocal boundary value problems of higher-order nonlinear fractional differential equations, Abstract and Applied Analysis, 200
• Arara A. el al., Fractional order differential equations on an unbounded domain, Nonlinear Anal. TMA (in press).
• Belmekki, M., Nieto, J.J., Rodriguez-Lopez, R., Existence of Periodic Solution for a Nonlinear Fractional Differential Equation, Boundary Value Problems, 2009.
• Bhaskar, T. G., Lakshmikantham, V., Leela, S., Fractional differential equations with Krasnoselskii-Krein-type condition, Nonlinear Analysis: Hybrid Systems, 2009.
• Lakshmikantham, V., Leela, S., Nagumo-type uniqueness result for fractional differential equations, Nonlinear Analysis 71, 2886-2889, 2009.
• Lakshmikantham, V., Leela, S., A Krasnoselskii-Krein-type uniqueness result for fractional differential equations, Nonlinear Analysis 71, 3421-3424, 2009.
• Lakshmikantham, V., Leela, S., Vasundhara Devi J., Theory of Fractional Dynamic Systems, Cambridge Scientific Publishers, 2009.