Ulam-Hyers Stability Of Two Classes Of Fractional Functional Differential Coupled Systems

Because the fractional order functional differential coupled system has the irre-placeable advantage of the integer order functional differential coupled system,the fractional order functional differential coupled system has attracted more and more attention.In this thesis,we mainly study the existence,uniqueness and stability of solutions for two kinds of fractional order functional differential coupled systems.For the first impulsive fractional differential coupled system with boundary con-ditions(?)(3)By means of Laplace transform,fixed point theorem,Mittag-Leffler function,the Beta(.,.)function and direct mathematical derivation,The existence,uniqueness and stabil-ity of solutions are obtained.For the second fractional order functional differential coupled with ?-Hilfer(?)(4)The existence,uniqueness and stability of the solution are obtained by using integral operator,fixed point theorem and direct mathematical derivation.This thesis broadens the application scope of fixed point theorem and mathemati-cal tools,and improves and generalizes others' models.Finally,two practical examples are given to illustrate the effectiveness of the results.