Solvability of impulsive $$(n,n-p)$$ ( n , n - p ) boundary value problems for higher order fractional differential equations

Abstract

We present a new general method for converting an impulsive fractional differential equation to an equivalent integral equation. Using this method and employing a fixed point theorem in Banach space, we establish existence results of solutions for a boundary value problem of impulsive singular higher order fractional differential equation. An example is presented to illustrate the efficiency of the results obtained. A conclusion section is given at the end of the paper.

Existence of Positive Solutions for a Nonlinear Higher-Order Multipoint Boundary Value Problem

“…In a recent paper [7], we study problems (1) and (2) with = 1 by a fixed point theorem of cone expansion and compression of functional type according to Avery et al [8]. For other existence results of positive solutions for higherorder multipoint problems, for a small sample of such work, we refer the reader to Ahmad and Ntouyas [9], Anderson et al [10], Davis et al [11], Du et al [12,13], Eloe and Henderson [14], Fu and Du [15], Graef et al [16,17], Henderson and Luca [18], Ji and Guo [19], Jiang [20], Liu et al [21], Liu and Ge [22], Liu et al [23], Palamides [24], Su and Wang [25], Zhang et al [26], and Zhang [27] and the references therein.…”