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Monotone and Concave Positive Solutions to a Boundary Value Problem for Higher-Order Fractional Differential Equation

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  • Jinhua Wang
  • Hongjun Xiang
  • Yuling Zhao

Abstract

We consider boundary value problem for nonlinear fractional differential equation ð · ð ›¼ 0 + ð ‘¢ ( ð ‘¡ ) + ð ‘“ ( ð ‘¡ , ð ‘¢ ( ð ‘¡ ) ) = 0 , 0 < ð ‘¡ < 1 , ð ‘› − 1 < ð ›¼ ≤ ð ‘› , ð ‘› > 3 , ð ‘¢ ( 0 ) = ð ‘¢ ′ ( 1 ) = ð ‘¢ î…ž î…ž ( 0 ) = ⋯ = ð ‘¢ ( ð ‘› − 1 ) ( 0 ) = 0 , where ð · ð ›¼ 0 + denotes the Caputo fractional derivative. By using fixed point theorem, we obtain some new results for the existence and multiplicity of solutions to a higher-order fractional boundary value problem. The interesting point lies in the fact that the solutions here are positive, monotone, and concave.

Suggested Citation

  • Jinhua Wang & Hongjun Xiang & Yuling Zhao, 2011. "Monotone and Concave Positive Solutions to a Boundary Value Problem for Higher-Order Fractional Differential Equation," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-14, September.
    • Handle: RePEc:hin:jnlaaa:430457
    DOI: 10.1155/2011/430457
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