Geodesic
Two-Point Boundary Value Problems for Fractional Differential Equations at Resonance
Bulletin of the Malaysian Mathematical Society, Tome 36 (2013) no. 3
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In this paper, by using the coincidence degree theory, we consider the following two-point boundary value problem for fractional differential equation \begin{equation*} \begin{cases} D_{0^+}^{\alpha}x(t)=f(t, x(t), x'(t)), t\in [0,1], \\ x(0)=0,\ x'(0)=x'(1), \end{cases} \end{equation*} where $D_{0^+}^\alpha$ denotes the Caputo fractional differential operator of order $ \alpha $, $1 \alpha \leq 2$. A new result on the existence of solutions for above fractional boundary value problem is obtained.
Classification : 34A08, 34B15 
@article{BMMS_2013_36_3_a17,
     author = {Zhigang Hu and Wenbin Liu and Taiyong Chen},
     title = {Two-Point {Boundary} {Value} {Problems} for {Fractional} {Differential} {Equations} at {Resonance}},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2013},
     volume = {36},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2013_36_3_a17/}
}
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Zhigang Hu; Wenbin Liu; Taiyong Chen. Two-Point Boundary Value Problems for Fractional Differential Equations at Resonance. Bulletin of the Malaysian Mathematical Society, Tome 36 (2013) no. 3. http://geodesic.mathdoc.fr/item/BMMS_2013_36_3_a17/