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The Existence and Uniqueness of Solutions for a Class of Nonlinear Fractional Differential Equations with Infinite Delay

Author

Listed:
  • Azizollah Babakhani
  • Dumitru Baleanu
  • Ravi P. Agarwal

Abstract

We prove the existence and uniqueness of solutions for two classes of infinite delay nonlinear fractional order differential equations involving Riemann‐Liouville fractional derivatives. The analysis is based on the alternative of the Leray‐Schauder fixed‐point theorem, the Banach fixed‐point theorem, and the Arzela‐Ascoli theorem in Ω = {y : (−∞, b] → ℝ : y|(−∞,0] ∈ ℬ} such that y|[0,b] is continuous and ℬ is a phase space.

Suggested Citation

  • Azizollah Babakhani & Dumitru Baleanu & Ravi P. Agarwal, 2013. "The Existence and Uniqueness of Solutions for a Class of Nonlinear Fractional Differential Equations with Infinite Delay," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:592964
    DOI: 10.1155/2013/592964
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    References listed on IDEAS

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    1. Dumitru Băleanu & Octavian G. Mustafa & Ravi P. Agarwal, 2010. "Asymptotically Linear Solutions for Some Linear Fractional Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    2. Dumitru Baleanu & Octavian G. Mustafa & Ravi P. Agarwal, 2010. "Asymptotically Linear Solutions for Some Linear Fractional Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-8, December.
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    Cited by:

    1. Yanan Li & Shurong Sun & Zhenlai Han & Hongling Lu, 2013. "The Existence of Positive Solutions for Boundary Value Problem of the Fractional Sturm‐Liouville Functional Differential Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

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