Firstly, the surveys for studies on boundary value problems for higher order ordinary differential equations and for higher order fractional differential equations are given. Secondly a simple review for studies on solvability of boundary value problems for impulsive fractional differential equations is presented. Thirdly we propose four classes of higher order linear fractional differential eq...

This paper is devoted to the study of periodic boundary value problems for nonlinear third order di¤erential equations subjected to impulsive e¤ects. We provide su¢ cient conditions on the nonlinearity and the impulse functions that guarantee the existence of at least one solution. Our approach is based on a priori estimates, the method of upper and lower solutions combined with an iterative te...

In this paper, we investigate the existence and uniqueness of solution of the periodic boundary value problem for nonlinear impulsive fractional differential equation involving Riemann-Liouville fractional derivative by using Banach contraction principle.

This article concerns boundary-value problems of first-order nonlinear impulsive integro-differential equations: y′(t) + a(t)y(t) = f(t, y(t), (Ty)(t), (Sy)(t)), t ∈ J0, ∆y(tk) = Ik(y(tk)), k = 1, 2, . . . , p,

u(T ) = ∑m i=0 ∫ ti+1 ti g(s, u(s)) dqis, where Dqk are qk-derivatives (k = 0, 1, 2, . . . ,m), f, g ∈ C(J ×R, R), Ik ∈ C(R,R), J = [0, T ](T > 0), 0 = t0 < t1 < · · · < tk < · · · < tm < tm+1 = T , J ′ = J\{t1, t2, . . . , tm}, and ∆u(tk) = u(t + k ) − u(t − k ), u(t + k ) and u(t − k ) denote the right and the left limits of u(t) at t = tk (k = 1, 2, . . . ,m) respectively. The study of q-dif...

where F : [0, 1]×R → P(R) is a compact valued multivalued map, P(R) is the family of all subsets of R, k ∈ (0, π 2 ), 0 < t1 < t2 < . . . < tm < 1, Ik ∈ C(R,R) (k = 1, 2, . . . , m), ∆x|t=tk = x(t + k )− x(t − k ), x(t + k ) and x(t − k ) represent the right and left limits of x(t) at t = tk respectively, k = 1, 2, . . . , m. In the literature there are few papers dealing with the existence of ...

This paper is related to the existence and approximation of solutions for impulsive functional differential equations with periodic boundary conditions. We study the existence and approximation of extremal solutions to different types of functional differential equations with impulses at fixed times, by the use of the monotone method. Some of the options included in this formulation are differe...

In this article, we prove the existence of solutions to mixed twopoint boundary-value problem for impulsive differential equations by variational methods, in both resonant and the non resonant cases.