The Existence of Solutions for a Fractional 2 ð ‘š -Point Boundary Value Problems

Gang Wang, Wenbin Liu, Jinyun Yang, Sinian Zhu and Ting Zheng

Journal of Applied Mathematics, 2012, vol. 2012, 1-18

Abstract:

By using the coincidence degree theory, we consider the following 2 ð ‘š -point boundary value problem for fractional differential equation ð · ð ›¼ 0 + ð ‘¢ ( ð ‘¡ ) = ð ‘“ ( ð ‘¡ , ð ‘¢ ( ð ‘¡ ) , ð · ð ›¼ − 1 0 + ð ‘¢ ( ð ‘¡ ) , ð · ð ›¼ − 2 0 + ð ‘¢ ( ð ‘¡ ) ) + ð ‘’ ( ð ‘¡ ) , 0 < ð ‘¡ < 1 , ð ¼ 3 − ð ›¼ 0 + ð ‘¢ ( ð ‘¡ ) | ð ‘¡ = 0 = 0 , ð · ð ›¼ − 2 0 + ∑ ð ‘¢ ( 1 ) = ð ‘š − 2 ð ‘– = 1 ð ‘Ž ð ‘– ð · ð ›¼ − 2 0 + ð ‘¢ ( 𠜉 ð ‘– ∑ ) , ð ‘¢ ( 1 ) = ð ‘š − 2 ð ‘– = 1 ð ‘ ð ‘– ð ‘¢ ( 𠜂 ð ‘– ) , where 2 < ð ›¼ ≤ 3 , ð · ð ›¼ 0 + and ð ¼ ð ›¼ 0 + are the standard Riemann-Liouville fractional derivative and fractional integral, respectively. A new result on the existence of solutions for above fractional boundary value problem is obtained.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:841349

DOI: 10.1155/2012/841349

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