Existence Of Solutions For Two Classes Of Fractional Langevin Equations With Antiperiodic Boundary Value Problems

In recent years,the fractional Langevin equation has been widely used in physic-s,biological chemistry,economy,technology and mathematics,so it has been further studied.In this paper,we discuss the antiperiodic boundary value problem of frac-tional Langevin equations with Caputo derivative.In chapter 2,we discuss the existence of solutions to the following equations:where T is the positive constant.1<??2,0<??1,0<?-??1,1<?<a,? is the real number.CD?,CD?,CD? are respective ?,?? order Caputo fractional derivative,f?C([0,T]x R,R).The uniqueness and existence of solu-tions for antiperiodic boundary value problems of fractional differential equations mentioned above are discussed by using Banach contraction mapping principle and the fixed point theorem.At last,the main results are illustrated by examples.In chapter 3,based on the second chapter,the uniqueness and existence of solutions for fractional Langevin equations are discussed by introducing nonlinear terms:...