Positive solutions for a semipositone fractional boundary value problem with a forcing term

Abstract

The authors obtain sufficient conditions for the existence of at least one and two positive solutions of a higher order semipositone fractional boundary value problem with a forcing term in the differential equation. Examples are included to illustrate the results.MSC 2010 : Primary 35J65, 47J10

On the oscillation of fractional differential equations

“…[2,5,7,10,11]. A rigorous theory of FDE has been started quite recently, see for example -the books [4,9,11] and to mention only few papers related to ordinary FDE as [3,6,8]. Separately, there are many recent works related c 2012 Diogenes Co., Sofia pp.…”

Positive Solutions for a Fractional Boundary Value Problem with a Perturbation Term

“…In the next section, we will study some new sharper upper and lower estimates for the Green's function of BVP (1) (2) than the ones given in [21]. In Section 3, we employ the new estimate to obtain the existence of a positive solution of BVP (1) (2).…”

“…In Section 3, we employ the new estimate to obtain the existence of a positive solution of BVP (1) (2). The idea of this paper may trace to [21][22][23][24][25][26][27].…”

“…However, as a result of the unusual feature of the fractional calculus, the investigation on the Green's functions for fractional boundary value problems is still in the initial stage. Recently, based on the spectral theory, the authors in [21] give an associated Green's function for BVP (1) (2) as series of functions. This idea was also used in [22][23][24].…”

Existence of positive solutions to a higher order singular boundary value problem with fractional q-derivatives

“…The monographs [30], [31], [32], and [33] provide excellent sources for the theory and applications of fractional calculus. Among all the topics, the existence of positive solutions of boundary value problems (BVPs) for fractional differential equations is currently undergoing active investigation; see for example, [3], [4], [5], [6], [12], [16], [21], [22], [27], [28], [29], [35], [36] and the references therein.…”