Existence Of Solutions For Three Classes Of Boundary Value Problems Of Fractional Differential Equations

Boundary value problems for differential equations of fractional order have expanded in the last two decades and have been the subject of increasing research because of the effectiveness of different boundary value problems for fitting phenomena in practical engineering.The paper discusses the existence of solutions to the same marginal value problem under different conditions for the integral boundary value problem.In general,the thesis extends the existing work to some extent,and is divided into five chapters.In Chapter 1,the background of the thesis,the state of the art of research at home and abroad,and some important preparatory knowledge on definitions,properties and lemmas to be used in the thesis are briefly explained.In Chapter 2,the fractional order differential equations under the Katugampola fractional order integral boundary conditions are discussed,and the existence of unique solutions to the boundary problems is obtained by using the principle of contraction mapping.The Katugampola fractional order derivatives unify and generalize the Riemann-Liouville and Hadamard derivatives,Therefore,the previous results are enriched to some extent.In Chapter 3,the Dirichlet problem of fractional order impulsive differential equations with p-Laplacian operators is considered and a solution is obtained using the critical point theorem and the variational method.The problem is transformed into a differential equation of integer order when the nonlinear terms satisfy certain conditions and p = 2,? = 1.This type of problem is not yet widely discussed and the results obtained are therefore relatively new.In Chapter 4,the existence of multiple solutions to a class of p-Laplacian fractional order impulsive differential equations with derivative terms is solved under the guarantees of the variational method,the mountain pass lemma and the critical point theorem.In Chapter 5,the main results of the thesis are summarized and an outlook on the subsequent research is given.