一类非线性分数阶多点边值问题的可解性

研究下面一类非线性分数阶微分方程多点边值问题■通过应用Mawhin重合度理论得到解的存在性结果.此结论拓展了在分数阶多点边值问题这个领域的以前的结果.

Solvability of Solutions for a Class of Nonlinear FractionalMulti-Point Boundary Value Problems

This paper is concerned with the following nonlinear fractional differential equations multi-point boundary value problem D^α₀₊u(t) = f(t, u(t), D^α-1₀₊u(t), D^α-2₀₊u(t), D^α-3₀₊u(t)), t ∈(0,1),   u(0) = 0, D^α-1₀₊u(0)=∑^m_i=1α_iD^α-1₀₊u(ξ_i), D^α-2₀₊u(1)=∑_j=1ⁿβ_jD^α-2₀₊u(η_j), D^α-3₀₊u(1)-D^α-3₀₊u(0)=D^α-2₀₊u(1) 1/2D^α-1₀₊u(0). By applying Mawhin coincidence degree theory, we obtain the existence of the solutions for the problem. The results expand the previous ones in the field.