带有积分边值条件的分数阶微分包含解的存在性

Existence of solutions for fractional-order differential inclusion with integral boundary value problems

分数阶微分方程被广泛用于解决众多领域的工程问题,如新材料科学、流体力学、电子电路等.此外,在生物学、经济学、最优控制等学科通过建立微分包含模型,对一些实际问题进行理论分析和研究,近年来,有关带有边值条件的分数阶微分方程和分数阶微分包含的研究受到了广泛关注.对基于CABADA和WANG的一类分数阶微分方程正解的存在性进行了研究,将其单值结果推广到多值情形.利用多值映射的不动点定理,研究了如下带有积分边值条件的分数阶微分包含问题:CD0+αy(t)∈F(t,y(t)),t∈(0,1),α∈(2,3),y(0)=y'(0)=0,y(1)=λ∫10y(s)ds,得到了包含非线性项是凸和非凸2种情形的带有积分边值条件的分数阶微分包含解存在的充分条件.

Differential equations with fractional order have proved to be extensive application in engineering problems,including new material science,fluid mechanics,viscoelasticity mechanics,electronic circuit,analytical chemistry and so on.Furthermore,biology,economics,optimal control and some practical problems can be solved by establishing differential inclusion models for theoretical analysis and research.In recent years,the studies on fractional differential equations and fractional differential inclusions with boundary value problems have got much attention.Based on the study of the existence of solutions for a class of fractional differential equations proposed by CABADA and WANG,we extend their results to cover the multivalued case.In this paper,based on the fixed-point theorem for multi-value maps,we have studied the following fractional order differential inclusions with integral boundary value problems：^CD0＋^αy（t）∈F（t,y（t））,t∈（0,1）,α∈（2,3）,y（0）=y＇（0）=0,y（1）=λ∫0^1y（s）ds.The sufficient conditions for the existence of solutions to the fractional order differential inclusions with integral boundary value conditions are established.Our results include the cases when the nonlinearity is convex as well as non-convex valued.