Existence Of Solutions For Two Classes Of Fractional Equations

The research on the existence and other properties of the solutions of fractional equations has very important significance and value.This paper mainly studies two types of fractional equations,namely: the existence of approximate solutions to a class of fractional multi-point boundary value problems with derivative terms is studied through mixed monotone fixed point theorems,and the existence of approximate solutions is studied through the Ekeland variational method.The multiple solutions of p-q-Laplace equations with sign potential and singular nonlinear term.This paper studies the existence and uniqueness of nontrivial solutions to the following fractional boundary value problems:By establishing a new mixed monotonic fixed point theorem,it is proved that problem(1)has a unique solution,and the corresponding iterative sequence is constructed to approximate the unique solution.At the same time,we study the following fractional p-q-Laplace equations with variable sign potential and singular nonlinear terms:Through the Nehari manifold method and some analysis methods,the multiplicity of the solutions of the above problem is obtained,and one of the solutions is the ground state solution.The sufficient conditions under which this problem has two positive solutions are given.