Abstract
In this paper, we consider the iterative properties of positive solutions for a general Hadamard-type singular fractional turbulent flow model involving a nonlinear operator. By developing a double monotone iterative technique we firstly establish the uniqueness of positive solutions for the corresponding model. Then we carry out the iterative analysis for the unique solution including the iterative schemes converging to the unique solution, error estimates, convergence rate and entire asymptotic behavior. In addition, we also give an example to illuminate our results.
Highlights
In recent years, many researchers were interested in the study of turbulent flow in which the fluid undergoes irregular fluctuations or mixing
In this paper, we choose a general Hadamard-type singular fractional differential equation involving a nonlinear operator from turbulent flow to study, we consider the iterative properties of positive solutions for the equation
By using the fixed point theorem of the mixed monotone operator Zhang et al [22] studied the uniqueness of positive solution for a fractional-order model of turbulent flow in a porous medium
Summary
Many researchers were interested in the study of turbulent flow in which the fluid undergoes irregular fluctuations or mixing. In this paper, we choose a general Hadamard-type singular fractional differential equation involving a nonlinear operator from turbulent flow to study, we consider the iterative properties of positive solutions for the equation. By using the fixed point index and the properties of nonnegative matrices Ding et al [9] considered the existence of positive solutions for a system of the above Hadamard-type fractional differential equations with semipositone nonlinearities. By using the fixed point theorem of the mixed monotone operator Zhang et al [22] studied the uniqueness of positive solution for a fractional-order model of turbulent flow in a porous medium. A fluid in highly heterogeneous porous media may push the transmission process from a phase into another different phase or state At absolute zero, this change always leads to transformation process losing continuity and further forms some singular points or singular domains.
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