| In recent years,the boundary value problem of fractional differential equations has received highly attention of the domestic and foreign mathematics and natural science field,and becomes one of the hottest issues in the international research field.The study of boundary value problem of fractional differential equation has important significance in both theoretical and applications.Many scholars have applied the theory and method of nonlinear analysis to study the integral boundary value problem of fractional differential equations on infinite intervals,and a large number of results have been obtained.In this paper,we mainly study the existence of solutions for integral boundary value problems of fractional differential equations on infinite intervals.This paper is divided into the following two chapters:In Chapter 1,we study the fractional differential equation integral boundary value problem involving derivatives on the infinite interval:where 2<?<?3,?>0,?,? ? 0,?(? + ?)>???+?-1,f?([0,?)×(-?,+?)×(-?,+?)×(-?,+?)×(-?,+?)),D0+?,D0+?-1?D0+?-2 are the Riemann-Liouville fractional derivatives,I0+? is the Riemann-Liouville fractional integral of order ?.By constructing the proper function space and the norm,we overcome the difficulty following from the noncompactness of[0,?).The existence and uniqueness results of solution are obtained by using the Schauder fixed point theorem and Banach contracting mapping principle.In Chapter 2,we study the existence of positive solutions of fractional semipositone integral boundary value problem on the half-line:where cD? is the Caputo fractional derivative of order ??(0,1),p ?C1([0,+?),(0,+?))?L1[0,+?),q:(0,+?)?(-?,+?)is Lebesgue integrable function,f:(0,+?)×[0,+?)?[0,+?)is a continuous function and may be singular at t = 0;?i:(0,+?)?[0,+?)is Lebesgue integrable function,?i>0,?i>0,i=1,2.The existence of positive solution is established by applying the fixed point index theory. |
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