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A Note on Fractional Equations of Volterra Type with Nonlocal Boundary Condition

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  • Zhenhai Liu
  • Rui Wang

Abstract

We deal with nonlocal boundary value problems of fractional equations of Volterra type involving Riemann‐Liouville derivative. Firstly, by defining a weighted norm and using the Banach fixed point theorem, we show the existence and uniqueness of solutions. Then, we obtain the existence of extremal solutions by use of the monotone iterative technique. Finally, an example illustrates the results.

Suggested Citation

  • Zhenhai Liu & Rui Wang, 2013. "A Note on Fractional Equations of Volterra Type with Nonlocal Boundary Condition," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:432941
    DOI: 10.1155/2013/432941
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    References listed on IDEAS

    as
    1. Fang Wang & Zhen-hai Liu & Jing Li, 2013. "Complete Controllability of Fractional Neutral Differential Systems in Abstract Space," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-11, February.
    2. Xiaoyou Liu & Zhenhai Liu, 2012. "Existence Results for Fractional Differential Inclusions with Multivalued Term Depending on Lower‐Order Derivative," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    3. Fang Wang & Zhen-hai Liu & Jing Li, 2013. "Complete Controllability of Fractional Neutral Differential Systems in Abstract Space," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
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