一类非线性分数阶多点边值问题的可解性

Abstract

Abstract:

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.

Key words: Fractional differential equation, Boundary value problem, Coincidence degree theory, Solvability of the solutions

CLC Number:

34B10

HAO Xiao-Hong, CHENG Zhi-Long, ZHOU Zong-Fu. Solvability of Solutions for a Class of Nonlinear Fractional Multi-Point Boundary Value Problems[J].Acta mathematica scientia,Series A, 2014, 34(3): 655-668.

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

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