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Existence and Uniqueness of Solution for a Class of Nonlinear Fractional Order Differential Equations

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  • Azizollah Babakhani
  • Dumitru Baleanu

Abstract

We discuss the existence and uniqueness of solution to nonlinear fractional order ordinary differential equations , with boundary conditions or satisfying the initial conditions , where denotes Caputo fractional derivative, is constant, and . Schauder's fixed-point theorem was used to establish the existence of the solution. Banach contraction principle was used to show the uniqueness of the solution under certain conditions on .

Suggested Citation

  • Azizollah Babakhani & Dumitru Baleanu, 2012. "Existence and Uniqueness of Solution for a Class of Nonlinear Fractional Order Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-14, June.
    • Handle: RePEc:hin:jnlaaa:632681
    DOI: 10.1155/2012/632681
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    Cited by:

    1. Alijani, Zahra & Baleanu, Dumitru & Shiri, Babak & Wu, Guo-Cheng, 2020. "Spline collocation methods for systems of fuzzy fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    2. Hasan, Shatha & Al-Smadi, Mohammed & El-Ajou, Ahmad & Momani, Shaher & Hadid, Samir & Al-Zhour, Zeyad, 2021. "Numerical approach in the Hilbert space to solve a fuzzy Atangana-Baleanu fractional hybrid system," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).

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