Existence of solutions for fractional anti-periodic BVP. (English) Zbl 1327.34010
From the summary and introduction: We consider the following anti-periodic boundary value problem for fractional differential equations
\[
\begin{gathered} {^cD^\alpha}x(t)+\lambda x(t)= f(t,x(t), x'(t)),\qquad 1<\alpha<2,\quad t\in J,\\ x(0)+ x(1)= 0,\qquad x'(0)+ x'(1)= 0,\end{gathered}
\]
where \(1<\alpha<2\) is a real number and \({^cD^\alpha}\) is the Caputo’s fractional derivative, \(J= [0,1]\), \(\lambda>0\) \(f:J\times\mathbb{R}\times \mathbb{R}\to\mathbb{R}\) is a given function.
The existence and uniqueness of solutions are obtained by using some fixed point theorems.
The existence and uniqueness of solutions are obtained by using some fixed point theorems.
MSC:
| 34A08 | Fractional ordinary differential equations |
| 34B15 | Nonlinear boundary value problems for ordinary differential equations |
| 47N20 | Applications of operator theory to differential and integral equations |
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