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In this article, we consider the parametric high-order fractional system with integral boundary value conditions involving derivatives of order $ p $-$ q $. With the aid of the fixed-point theorem, an exact interval from the existence to the solution of the system will be obtained, under the condition that the nonlinearities of the system may have singularities. Finally, we provide an instance to show the practicality of the primary outcomes.

In this paper we use the fixed point index theory to study the existence of positive radial solutions for a system of boundary value problems with semipositone second order elliptic equations. Some appropriate concave and convex functions are utilized to characterize coupling behaviors of our nonlinearities.

In this paper, the maximal and minimal iterative positive solutions are investigated for a singular Hadamard fractional differential equation boundary value problem with a boundary condition involving values at infinite number of points. Green's function is deduced and some properties of Green's function are given. Based upon these properties, iterative schemes are established for approximating the maximal and minimal positive solutions.