具有适型分数阶导数的边值问题的正解

Abstract

Abstract:

In this paper, we establish the solvability of a class nonlinear fractional differential equation boundary value problem D^αu(t)+f(t, u(t))=0, 0 < t < 1, u(0)=u(1)=0, where 1 < α ≤ 2 is a real number, D^α is the conformable fractional derivative, and f:[0, 1]×[0, ∞)→[0, ∞) is a continuous function. One of the difficulty here is the corresponding Green's function G(t, s) is singular at s=0. By the use of approach method and fixed-point theorems on cone, some existence and multiplicity results of positive solutions are acquired.

Key words: Conformable fractional derivative, Singular Green's function, Fixed-point theorems on cone

CLC Number:

O175.08

Dong Xiaoyu, Bai Zhanbing, Sun Sujing. Positive Solutions for Some Boundary Value Problems with Conformable Fractional Differential Derivatives[J].Acta mathematica scientia,Series A, 2017, 37(1): 82-91.

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References

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Positive Solutions for Some Boundary Value Problems with Conformable Fractional Differential Derivatives

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