The uniqueness and iterative properties of solutions for a general Hadamard-type singular fractional turbulent flow model

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.

Iterative Hille‐type oscillation criteria of half‐linear advanced dynamic equations of second order

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An Efficient Numerical Method Based on Bell Wavelets for Solving the Fractional Integro-Differential Equations with Weakly Singular Kernels

“…There are usually three definitions of fractional calculus: Riemann-Liouville fractional calculus, Grünwald-Letnikov's fractional calculus, and Caputo fractional calculus. In recent years, many studies have focused on the existence, regularity, and convergence of solutions to fractional differential equations [3][4][5][6]. However, it is difficult to obtain analytical solutions for fractional differential equations or fractional integral differential equations.…”

Upper and Lower Solution Method for a Singular Tempered Fractional Equation with a p-Laplacian Operator

“…On the other hand, a p-Laplacian equation can model turbulent flow in a porous medium [11][12][13][14][15]; in particular, when the equation contains tempered fractional derivatives, it can model turbulent velocity fluctuations of porous medium with features of power-law behavior at infinity and infinite divisibility [16]. Therefore, in the process of analyzing the statistical data and and modeling the basic physical phenomena in turbulent flow, Brownian motion, tempered Lévy flight, tempered stable laws are an useful tool.…”

“…Due to the widespread application of differential equations in practice, in recent decades, many theories and methods of nonlinear analysis, such as the spaces theories [26][27][28][29][30][31], smoothness theories [32][33][34][35], operator theories [36][37][38], fixed-point theorems [18,21,24,25,[39][40][41], subsuper solution methods [17,[42][43][44][45], monotone iterative techniques [12,[46][47][48][49][50][51][52][53] and the variational method [54][55][56][57][58], have been developed to study various differential equations. For example, by adopting the fixed point theorem of the mixed monotone operator, Zhou et.…”