Positive solutions for singular nonlinear fractional differential equation with integral boundary conditions

Hongdan Li, Lishan Liu, Yonghong Wu
2015 Boundary Value Problems  
In this article, we study the existence of positive solutions for a class of singular nonlinear fractional differential equations with Riemann-Stieltjes integral boundary conditions. Using the properties of the Green function and the fixed point theory in cones, we obtain some results on the existence of positive solutions. Our results extend and improve many known results including singular and nonsingular cases. MSC: 34A08; 34B16; 34B18 Keywords: singular fractional differential equations;
more » ... ntial equations; Riemann-Stieltjes integral boundary value problem; positive solution; multiple positive solutions; fixed point theorem in cone   h(s)u(s) dA(s) denotes the Riemann-Stieltjes integral with a signed measure, in which A : [, ] → R is a function of bounded variation. Fractional differential equations have attracted more and more attention from the research communities due to their numerous applications in many fields of science and engineering including fluid flow, rheology, diffusive transport akin to diffusion, electrical networks, probability, etc. For details, see [-] and the references therein. On the other hand, boundary value problems with integral boundary conditions for ordinary differential equations arise in many fields of applied mathematics and physics such as heat conduction, chemical engineering, underground water flow, thermoelasticity, and plasma physics. The existence and multiplicity of positive solutions for such problems have become an important area of investigation in recent years.
doi:10.1186/s13661-015-0493-3 fatcat:t6ofg4hdmvf7pepj5gh7diftge