Explicit Iteration and Unique Positive Solution for a Caputo-Hadamard Fractional Turbulent Flow Model

• Main Authors: Guotao Wang, Xueyan Ren, Lihong Zhang, Bashir Ahmad
• Format: Article
• Language: English
• Published: IEEE 2019-01-01
• Series: IEEE Access
• Subjects: Caputo-Hadamard fractional turbulent flow model; Erdélyi-Kober fractional integral operator; mixed monotone operator; <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">p(t)</italic>-Laplacian operator
• Online Access: https://ieeexplore.ieee.org/document/8792122/

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-Hadamardtype fractional turbulent flow model involving p(t)-Laplacian operator and Erde&#x0301;lyi-Kober fractional integral operator. Thep(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 Erde&#x0301;lyi-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.