The existence of solutions for nonlinear fractional boundary value problem and its Lyapunov-type inequality involving conformable variable-order derivative

Journal of Inequalities and Applications

Jie Wang¹  Shuqin Zhang¹ 

[1] School of Science, China University of Mining and Technology;

关键词: Lyapunov-type inequality;    Conformable variable-order derivative;    Green’s function;    Boundary value problem;    Upper and lower solutions’ method;   

DOI  :  10.1186/s13660-020-02351-7

来源: DOAJ

【 摘 要 】

Abstract We consider a nonlinear fractional boundary value problem involving conformable variable-order derivative with Dirichlet conditions. We prove the existence of solutions to the considered problem by using the upper and lower solutions’ method with Schauder’s fixed-point theorem. In addition, under some assumptions on the nonlinear term, a new Lyapunov-type inequality is given for the corresponding boundary value problem. The obtained inequality provides a necessary condition for the existence of nontrivial solutions to the considered problem and a method to prove uniqueness for the nonhomogeneous boundary value problem. These new results are illustrated through examples.

【 授权许可】

Unknown