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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 (𝒟α − ρt𝒟β)x(t) = f(t, x(t), 𝒟γx(t)), t ∈ (0, 1) with boundary conditions x(0) = x0, x(1) = x1 or satisfying the initial conditions x(0) = 0, x′(0) = 1, where 𝒟α denotes Caputo fractional derivative, ρ is constant, 1

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, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:632681
    DOI: 10.1155/2012/632681
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    References listed on IDEAS

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    1. Azizollah Babakhani, 2010. "Positive Solutions for System of Nonlinear Fractional Differential Equations in Two Dimensions with Delay," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-16, May.
    2. Azizollah Babakhani, 2010. "Positive Solutions for System of Nonlinear Fractional Differential Equations in Two Dimensions with Delay," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    3. A. Babakhani & E. Enteghami, 2009. "Existence of Positive Solutions for Multiterm Fractional Differential Equations of Finite Delay with Polynomial Coefficients," Abstract and Applied Analysis, Hindawi, vol. 2009, pages 1-12, October.
    4. Azizollah Babakhani & Dumitru Baleanu, 2011. "Existence of Positive Solutions for a Class of Delay Fractional Differential Equations with Generalization to N‐Term," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    5. A. Babakhani & E. Enteghami, 2009. "Existence of Positive Solutions for Multiterm Fractional Differential Equations of Finite Delay with Polynomial Coefficients," Abstract and Applied Analysis, John Wiley & Sons, vol. 2009(1).
    6. Azizollah Babakhani & Dumitru Baleanu, 2011. "Existence of Positive Solutions for a Class of Delay Fractional Differential Equations with Generalization to N-Term," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-14, June.
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    Cited by:

    1. A. G. Radwan & K. Moaddy & I. Hashim, 2013. "Amplitude Modulation and Synchronization of Fractional‐Order Memristor‐Based Chua′s Circuit," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. F. A. Abd El-Salam, 2013. "N‐Dimensional Fractional Lagrange′s Inversion Theorem," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

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