Abstract
Abstract In this paper, we consider the existence of positive solutions for a singular fractional differential system involving a nonlocal boundary condition which is given by a linear functional on C [ 0 , 1 ] with a signed measure. By looking for the upper and lower solutions of the system, the sufficient condition of the existence of positive solutions is established; some further cases are discussed. This is proved in the case of strong singularity and with a signed measure. MSC:34B15, 34B25.
Highlights
1 Introduction In this paper, we consider the existence of positive solutions for a singular nonlinear fractional differential system with nonlocal boundary conditions
In system ( . ), the boundary condition is given by a nonlocal condition involving a Stieltjes integral type linear functional on C[, ] with a signed measure, but it does not need to be a positive functional
Since the nonlocal boundary value problems can describe a class of very interesting and important phenomena arising from heat conduction, chemical engineering, underground water flow, thermo-elasticity, and plasma physics, this type of problem has attracted much attention of many researchers
Summary
1 Introduction In this paper, we consider the existence of positive solutions for a singular nonlinear fractional differential system with nonlocal boundary conditions, Based on the fixed point theory of a strict set of contraction operators in a cone, Feng et al [ ] investigated the existence and nonexistence of positive solutions of the following second order BVPs with integral boundary conditions in Banach space:
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