Abstract
In this paper, we are concerned with the existence of the maximum and minimum iterative solutions for a tempered fractional turbulent flow model in a porous medium with nonlocal boundary conditions. By introducing a new growth condition and developing an iterative technique, we establish new results on the existence of the maximum and minimum solutions for the considered equation; at the same time, the iterative sequences for approximating the extremal solutions are performed, and the asymptotic estimates of solutions are also derived.
Highlights
Tempered stable laws were introduced to model turbulent velocity fluctuations of physics [1]
In [3], an exponential tempering factor was applied to the particle jump density in random walk and stochastic model for turbulence in the inertial range, which is the fractional derivative of Brownian motion exhibiting semilong range dependence with a power law at moderate time scales
Tempered stable laws are useful in statistical physics and provide a basic physical model such as turbulent flow for the underlying physical phenomena
Summary
Tempered stable laws were introduced to model turbulent velocity fluctuations of physics [1]. Tempered stable laws are useful in statistical physics and provide a basic physical model such as turbulent flow for the underlying physical phenomena Motivated by these physical backgrounds and the sources, in this paper, we focus on the existence of the maximum and minimum iterative solutions for the following tempered fractional turbulent flow equation with nonlocal boundary conditions:. Us, following the previous work, this paper will pay attention to the extremal solutions for the tempered fractional turbulent flow equation in a porous medium with nonlocal Riemann–Stieltjes integral boundary conditions by developing iterative technique, see [97,98,99,100]. The iterative sequences for approximating the extremal solutions are performed, and the asymptotic estimates of solutions are obtained
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