| The characteristics of memory and non-locality of fractional derivatives enable the frac-tional differential equation model to simply and accurately describe complex systems and behaviors in nature.Fractional differential equations are widely used in biomedical engineer-ing,system control and other fields.Many problems in these fields can be abstracted as boundary value problems of fractional differential equations with mixed monotone nonlinear terms.In this paper,the basic theory of nonlinear functional analysis,especially the fixed point theory of nonlinear operators,are used to obtain existence of related conclusions of the fixed points of two types of mixed monotone operators,without the existence of upper and lower solutions or compactness and continuity of operator.In addition,the fixed point theory of mixed operators are used to study the existence and uniqueness of solutions of Riemann–Liouville fractional differential equations with mixed monotone nonlinear terms.The main results are listed as follows:Firstly,a sufficient condition for the existence of fixed points of mixed monotone operators based on the set Ph,e is given,and the results are used to study the existence and uniqueness of solutions for a class of two-point boundary value problems of fractional differential equations.And given an example to verify the correctness of the results.Secondly,the related results of the existence of sum type mixed monotone operators fixed points of are given,and the results obtained are used to study for a class of boundary value problems of fractional differential equations with integral boundary,the existence and uniqueness of the solution of the equation is obtained,and an example is given as a verification.Finally,the existence and uniqueness of the solution of a class of fractional differential equations with multi-point boundary value problem is studied,and the feasibility of the result is verified with specific examples. |
PDF Full Text Request