The Iterative Properties for Positive Solutions of a Tempered Fractional Equation

In this article, we investigate the iterative properties of positive solutions for a tempered fractional equation under the case where the boundary conditions and nonlinearity all involve tempered fractional derivatives of unknown functions. By weakening a basic growth condition, some new and complete results on the iterative properties of the positive solutions to the equation are established, which include the uniqueness and existence of positive solutions, the iterative sequence converging to the unique solution, the error estimate of the solution and convergence rate as well as the asymptotic behavior of the solution. In particular, the iterative process is easy to implement as it can start from a known initial value function.

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In this article, the iterative properties of positive solutions for a tempered fractional equation are investigated. By weakening a basic growth condition, new and complete results on the iterative properties of the positive solutions to the equation are established, including the uniqueness and existence of positive solutions, the convergence of the iterative sequence to the unique solution, the error estimate and convergence rate of the solution, as well as the asymptotic behavior of the solution.