Abstract
The uniqueness of positive solution for a class of singular fractional differential system with integral boundary conditions is considered in this paper and many types of equation system are contained in this equation system because there are many parameters which can be changeable in this equation system. The fractional orders are involved in the nonlinearity of the boundary value problem and the nonlinearity is allowed to be singular in regard to not only time variable but also space variable. The existence of uniqueness of positive solution is mainly obtained by fixed point theorem of mixed monotone operator and the positive solution of equation system is dependent on λ. An iterative sequence and convergence rate are given which are important for practical application and an example is given to demonstrate the validity of our main results.
Highlights
In the past couple of decades, boundary value problems for nonlinear fractional differential equations arise from the studies of complex problems in many disciplinary areas such as aerodynamics, fluid flows, electrodynamics of complex medium, electrical networks, rheology, polymer rheology, economics, biology chemical physics, control theory, signal and image processing, blood flow phenomena, and so on
The authors obtained the uniqueness of a positive solution by using the fixed point theorem of the mixed monotone operator
Many papers are devoted to the fractional differential equations in which the fractional orders are involved in the nonlinearity; see [, – ]
Summary
In the past couple of decades, boundary value problems for nonlinear fractional differential equations arise from the studies of complex problems in many disciplinary areas such as aerodynamics, fluid flows, electrodynamics of complex medium, electrical networks, rheology, polymer rheology, economics, biology chemical physics, control theory, signal and image processing, blood flow phenomena, and so on. The authors obtained the existence and multiplicity of positive solutions by means of Krasnosel’skii’s fixed point theorem. The p-Laplacian operator is defined as φp(s) = |s|p– s, p > , and the nonlinearity f (t, u, v) may be singular at both u = and v = , and Dαt , Dβt , Dγt are the standard Riemann-Liouville derivatives.
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