Abstract
Hadamard fractional calculus theory has made many scholars enthusiastic and excited because of its special logarithmic function integral kernel. In this paper, we focus on a class of Caputo-Hadamard-type fractional turbulent flow model involving p(t)-Laplacian operator and ErdClyi-Kober fractional integral operator. The p(t)-Laplacian operator involved in our model is the non-standard growth operator which arises in many fields such as elasticity theory, physics, nonlinear electrorheological fluids, ect. It is the first paper that studies a Caputo-Hadamard-type fractional turbulent flow model involving p(t)-Laplacian operator and ErdClyi-Kober fractional integral operator. Different from the constant growth operator, The non-standard growth characteristics of p(t)-Laplacian operator bring great difficulties and challenges. In order to achieve a good survey result, we take advantage of the popular mixed monotonic iterative technique. With the help of this approach, we obtain the uniqueness of positive solution for the new Caputo-Hadamard-type fractional turbulent flow model. In the end, an example is also given to illustrate the main results.