Existence of solutions for a three-point Hadamard fractional resonant boundary value problem. (English) Zbl 1527.34017
In this article, the authors study a class of three point boundary value problems of Hadamard fractional nonlinear differential equation as
\[
\begin{cases} (^H D^\alpha_{a^+}u)(t)=f(t,u,^{H} D^{\alpha-1}_{a^+}u)),~~ 1<\alpha\leq 2,~0<a<t<b, \\
(^{H} D^{\alpha-2}_{a^+}u)(a)=0,~~\eta u(\xi)=u(b),~~ a<\xi<b,~\eta>0, \end{cases}
\]
where the parameters satisfy
\[
(\log\frac{b}{a})^{\alpha-1}=\eta (\log\frac{\xi}{a})^{\alpha-1}.
\]
The existence of solutions for the boundary value problems is established, and is proven by using the theory of coincidence degree. Finally, a numerical example is provided to illustrate the theoretical results obtained.
The existence of solutions for the boundary value problems is established, and is proven by using the theory of coincidence degree. Finally, a numerical example is provided to illustrate the theoretical results obtained.
Reviewer: Xiping Liu (Shanghai)
MSC:
| 34A08 | Fractional ordinary differential equations |
| 34B10 | Nonlocal and multipoint boundary value problems for ordinary differential equations |
| 34B15 | Nonlinear boundary value problems for ordinary differential equations |
| 47H11 | Degree theory for nonlinear operators |
Keywords:
fractional differential equations; Hadamard fractional derivatives; nonlinear boundary value problems; multi-point boundary conditions; resonance; existence; coincidence degree theoryReferences:
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