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Volume 10, Number 5, 2020, Pages 1937-1953                                                                DOI:10.11948/20190289
Solvability for Riemann-Stieltjes integral boundary value problems of Bagley-Torvik equations at resonance
Nan Yao,Xiping Liu,Mei Jia
Keywords:Bagley-Torvik equation, Caputo derivative, Riemann-Stieltjes integral, boundary value problem, resonant condition, Mawhin''s coincidence degree theory.
Abstract:
      In this paper, we study the solvability for Riemann-Stieltjes integral boundary value problems of Bagley-Torvik equations with fractional derivative under resonant conditions. Firstly, the kernel function is presented through the Laplace transform and the properties of the kernel function are obtained. And then, some new results on the solvability for the boundary value problem are established by using Mawhin''s coincidence degree theory. Finally, two examples are presented to illustrate the applicability of our main results.
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