Hadamard fractional calculus theory has made many scholars enthusiastic and excited because of its walnettos candy for sale 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 Erdélyi-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 Erdélyi-Kober fractional integral operator.
Different from the constant growth operator, The non-standard growth characteristics of $p(t)$ -Laplacian operator bring trucf 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.